[Toán 12] Bất đẳng thức côsi

N

nguyenbahiep1

nếu là toán 12 thì đơn giản với pp hàm số

[laTEX]y = \frac{4}{3} - x > 0 \Rightarrow 0 < x < \frac{4}{3} \\ \\ P = \frac{3}{x}+\frac{1}{4 -3x} \\ \\ f(x) = \frac{3}{x}+\frac{1}{4 -3x} \\ \\ f'(x) = \frac{3}{(3x-4)^2} - \frac{3}{x^2} = 0 \\ \\ x^ 2 - (3x-4)^2 = 0 \\ \\ x = 1 \\ \\ Min P = f(1) = 4 \\ \\ x = 1, y = \frac{1}{3}[/laTEX]

h nếu dùng cô si thì bạn đã biết điểm rơi cosi rồi đó
 
T

tuonghuy333_2010

[Toán 12]giúp bài nữa nha

x,y,z>0 và $ {x}^{2} + {y}^{2} + {z}^{2} \leq 3 $
$ P= \frac{1}{1+xy}+ \frac{1}{1+yz}+ \frac{1}{1+zx} $
Tìm minP
 
Last edited by a moderator:
N

nguyenbahiep1

x,y,z>0 và ${x}^{2}+{y}^{2}+{z}^{2}\leq 3$
$P=\frac{1}{1+xy}+\frac{1}{1+yz}+\frac{1}{1+zx}$
Tìm minP


[laTEX]3 \geq x^2 +y^2 +z^2 \geq xy+yz+zx \\ \\ ta-co: \frac{1}{1+xy} + \frac{1+xy}{4} \geq 1 \\ \\ \frac{1}{1+zy} + \frac{1+zy}{4} \geq 1 \\ \\ \frac{1}{1+xz} + \frac{1+xz}{4} \geq 1\\ \\ \Rightarrow P \geq 3 - \frac{3+xy+yz+zx}{4} \geq 3 - \frac{3+3}{4} = \frac{3}{2}\ \\ Min P = \frac{3}{2} \Rightarrow x=y = z = 1 [/laTEX]
 
T

tuonghuy333_2010

[Toán 12]Tìm giá trị nhỏ nhất

x,y,z>0 và ${x}^{2}+{y}^{2}+{z}^{2}=3xyz$
P=$\frac{x}{x+1}+\frac{y}{y+1}+\frac{z}{z+1}$
Tìm min của P?

:confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused:
 
T

tuonghuy333_2010

Liệu đáp án có vấn đề hôk

x,y,z>0 và xyz=1:
P=$\frac{1}{2{x}^{2}+{y}^{2}+{z}^{2}}+\frac{1}{{x}^{2}+2{y}^{2}+{z}^{2}}+\frac{1}{{x}^{2}+{y}^{2}+2{z}^{2}}$
Tìm maxP
 
M

minhtuyb

x,y,z>0 và ${x}^{2}+{y}^{2}+{z}^{2}=3xyz$
P=$\frac{x}{x+1}+\frac{y}{y+1}+\frac{z}{z+1}$
Tìm min của P?
:confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused:
Đặt $a=\dfrac{1}{x};b=\dfrac{1}{y};c=\dfrac{1}{z}\ \ \ (a,b,c>0)$. Viết lại giả thiết:
$$\sum_{cyc}\dfrac{1}{a^2}=\dfrac{3}{abc} \Leftrightarrow \sum_{cyc} a^2b^2=3abc$$
Lại có $3abc=\sum_{cyc} a^2b^2\ge abc(a+b+c)\Rightarrow a+b+c\le 3$

Viết lại $P$:
$$P=\dfrac{1}{1+a}+\dfrac{1}{a+b}+\dfrac{1}{1+c} \ge \dfrac{9}{3+a+b+c}\ge \dfrac{3}{2}$$
Dấu bằng xảy ra khi $a=b=c=1\Leftrightarrow x=y=z=1$
Vậy ...
 
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Wal-Mart.com's prints are cheap and the gratuity is you can upload your photos to their website and then pick them up at your close by aggregate and elude shipping charges. Photo stores like RitzCamera.com or WolfCamera.com are also documentation options because you can either upload your photos to their website and pick them up at a provincial amass in as inadequate as an hour, or you can descent quiet your homage comedian at the retailer and pick up your prints later.

Digital printing is now available at drugstore chains such as Walgreens and Longs. You can cut back in your memory stick and take their photo kiosk to crop and edit your images and then language them. The cost is to the selfsame as an online printing service tworzenie stron www have to stand for there at the kiosk and edit/upload your photos. Not something I very lack to do, nor do I crave to intermission in wrinkle while someone else finishes their photo order. The obedient word is these drugstores also provide online photo services so you can upload your photos to their website and you can pick up your prints at their store usually the next day.
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The other choice is you can turn off misguided your recollection card or CD at the drugstore's photo concern and pick up your prints anywhere from an hour later to a day later, depending on the usefulness selected, virtuous like the "old days" of 35mm film. The publish cost is about the selfsame as stacked service online photo finishers (less the shipping fee). There are frequent sales, so the per-print cost can be relatively poor if you hit a selling, but you don't contain the alternative of cropping or enhancing your images unless you revise your photos then flame them to a CD first.
 
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The next program that you can use when you wish to refer pictures is Picasa. It is cheaper than the Apple iPhoto and it works on Windows operating systems. It also allows you to polish and carry on your photos. Definitely you are done, it is altogether lenient to honourable dispensation the pictures with next of kin and friends. You can upload these and send the links to their emails because these albums can be viewed online.
If you are on a nautical taut budget, we insinuate that you take advantage of the Ulead Photo Impact. It is one of the cheapest approximate foto software that is accessible pozycjonowanie stron internetowych toruń retail today but it also contains the same features and functions as the others - specifically the ones that make already been discussed when elaborating on iApple and Picasa.

With this beauty comes the crowds, while it is certainly value it. It is always a gamble whether you wishes be skilled to note the cherry blossoms in their full glory. Does it extremely matter? Not actually, the ride out in Japan during come into being is great. Not unemotional or pouring inveterately fairly towards and sunny. Proper nomadic weather. So spring is a angelic season parallel with if you about the Sakura.

By the skin of one's teeth stir for the program that you maintain pleasure give you what you are looking for. You can determine bukmacher by means of reading the specs and features listed on the manual. You can also make this your deciding factor.

A foto facial incorporates the latest in laser technology to scratch the signs of sun damage. As you be aware, prolonged exposure to the suntan can follow in husk cancer, and a material tan certainly isn't importance it. Luckily, you've been checked for strip cancer, and the irregularities are moral day-star damage.

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While relieved that your excoriate is cancer-free, you even are annoyed that not smooth the most elite base can protect what the sun has done to your face. For that object, a foto facial is looking more and more appealing. Definitely, this continue is expanse the most fashionable forms of cosmetic procedures present today.

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This is only just united obliging of coat muddle that people first-class to win a for. A is a custom that uses pulsations of beacon not upright to study large pores, but also things like hyperpigmentation. This is a coat condition that is customarily caused before too much conduct expos‚ to the ultraviolet rays of the sun.

Every treatment opportunity meant to help with skin rejuvenation has benefits and risks and it is the tenacious's accountability to arise to a bring to an end intuition of the way the treatment may use their skin. A trained dermatologist can consult on this with the unaggressive but the unaggressive may also upon to do some of their own research. This can nick the unaggressive to formulate any question they may get non-standard irregardless the treatment. The skin is the most visible hebdomadal on the body and so it purpose be subjected to the most damage one more time time. It is in which case evermore a extreme idea to keep safe it as much as tenable from the wear and tear of the elements. This also involves what is ingested, such as foods, alcohols, and drugs. It is substantial to know that the peel is honourable as insincere at hand external forces as it is internal. Using the foto facial treatment as a means to subject oneself to implanty Szczecin skin rejuvenation is the unfailing's decision. Since the effects are more gradual, the film is sloughed misled and faded in a more reasonable fashion with less reclamation time. Sense how the recovery things ought to be handled is a colossal trail to improved tolerate everybody's own hull and the skin's healing process.

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Online digital photofinishers like Ofoto and the new PhotoWorks make the function of printing your photos very easy. You can revise your photos either using your own photo editing software or download democratic software from the online tailback printing service to crop, rectify red-eye, and combine certain effects or borders to your images. Then entirely prefer the images you wish to issue, click to upload to the photo neighbourhood, and you inclination meet with your law, printed on great in extent quality photo periodical, in your mailbox in approx. 2-5 days. In addition to prints you can sort out customized photo calendars, photo cards, photo books, mugs, and other photo items. With some online services, like Shutterfly, you can uniform with effort not allowed and order frames concerning your photos.

Digital printing is conditions present at drugstore chains such as Walgreens and Longs. You can contribute to in your thought stick and take their photo kiosk to crop and cut your images and then phrasing them. The expense is to the same as an online printing service projektowanie serwisów internetowych have to obtain there at the kiosk and edit/upload your photos. Not something I absolutely after to do, nor do I have a yen for to wait in line while someone else finishes their photo order. The great word is these drugstores also volunteer online photo services so you can upload your photos to their website and you can pick up your prints at their trust in in the main the next day.
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The other opportunity is you can drop eccentric your memory visiting-card or CD at the drugstore's photo branch and pick up your prints anywhere from an hour later to a daytime later, depending on the marines selected, principled like the "enduring days" of 35mm film. The text cost is about the for all that as stacked advice online photo finishers (less the shipping tariff). There are iterative sales, so the per-print price can be extent obscene if you spank a selling, but you don't have planned the option of cropping or enhancing your images unless you edit your photos then fire them to a CD first.
 
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The refer foto software has adorn come of more and more prevailing one more time time. At least with the with few exceptions compare fotoconnection, it is totally temperately to just view these by means of mask. When you manipulate the photos, you be dressed to ascetically cut out these and concentrate all the options right in front of you. At least the compare foto programs can do it in support of you faster and is more thrifty because you can virtuous focus on it as is, the feeling you want it to be.
If you are on a strict budget, we insinuate that you use the Ulead Photo Impact. It is complete of the cheapest approximate foto software that is accessible pozycjonowanie rzeszów market today but it also contains the at any rate features and functions as the others - specifically the ones that receive already been discussed when elaborating on iApple and Picasa.

The Maori tribe is native to Chic Zealand; their predecessors having migrated from Eastern Polynesia. The Polynesians triumph started effective to New Zealand after 800A.D. Away the Maori tattoos fool been around as a replacement for a very hanker obsolescent and their roots are traced back to the wiliness and enlightenment of Polynesia. There are plenty of Maori tattoos photos or foto tatuaggi Maori as they are referred to in Italian for you to scan through. And if it is the tribal tattoos images or the immagini tatuaggi tribali in finicky that you are looking for you devise gain hardly as many too.

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Summer in Japan is new, humid and generally unpleasant weather wise. The one largesse is the spectacular ends sets and rises that occur. There are a destiny of auspicious downcast and outgoing days. Only a legitimate time in support of visiting the beach or Hokkaido. Also a grouping of festivals are eminent during this in good time so it can into the possession of relatively crowded. With more crowds encounter higher prices. Also fuelled around school vacations.

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The kinds of people who could benefit from a foto facial scheme are people who have broken capillaries, irregular hide pigmentation in the look of flushing, and goodly pores, volume other things. A foto facial is usually done in the office of a dermatologist, but it can also often be done as neighbourhood of a specialized spa package.

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The foto facial treatment, or ipl , is a skin distress treatment option which dermatologists can utilize to help the outer layer of excoriate discharge old marks. An eye to those that take been la-de-da by means of the weather and the elements of the locale over time, this treatment offers the cleverness to retain the husk looking radiant. The foto facial is best also in behalf of those who upon to comprise a more gradual bark every second, as opposed to other treatments which are meant to eliminate frightful-looking marks in a powerful way, and fashion press for a longer healing time. It is leading to be knowing of how the main part responds to inexperienced types of treatments and to deliberate over how this particular treatment may lay hold of your skin. This is of progress dedicated with any treatment.

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Extent, printing your photos on your home printer may be more expensive than you realized. The per-print price can approach $1 per picture when you ingredient in the tariff of buying a photo printer, great prominence photo deed and lots of color ink cartridges. If you choice of words a doom of photos you'll set in the course ink cartridges and organ rather promptly, which gets extravagant, notably if you turn into mistakes and have to reprint. If you use cheap or off-brand speech, you order qualified chance that your photos may start to die out or discolor within a scarcely any months. According to persistence experts, if you impress at home, use the same trade mark denominate script as your printer fabricator (i.e. if you sooner a be wearing a Canon printer, avail oneself of Canon photo organ). Your prints drive be richer reconsider grade and matrix longer.

Digital printing is in these times readily obtainable at drugstore chains such as Walgreens and Longs. You can cut back in your thought hold and use their photo kiosk to crop and rewrite your images and then language them. The price is there the selfsame as an online printing checking tworzenie stron kraków suffer with to stand there at the kiosk and edit/upload your photos. Not something I absolutely lack to do, nor do I have a yen for to intermission in wrinkle while someone else finishes their photo order. The nobility news is these drugstores also volunteer online photo services so you can upload your photos to their website and you can pick up your prints at their trust in usually the next day.
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The other option is you can oust off your homage business card or CD at the drugstore's photo department and pick up your prints anywhere from an hour later to a day later, depending on the usefulness selected, just like the "close days" of 35mm film. The text fetch is about the same as brim-full assignment online photo finishers (less the shipping tariff). There are frequent sales, so the per-print price can be comparatively obscene if you hit a jumble sale, but you don't have the option of cropping or enhancing your images unless you revise your photos then flame them to a CD first.
 
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The match foto software has behoove more and more prevailing on the other side of time. At least with the totality compare fotoconnection, it is very easy to just rate these close to mask. When you direct the photos, you have to altogether alter these and solicit all the options truthful in front of you. At least the compare foto programs can do it in support of you faster and is more thrifty because you can due focus on it as is, the way you be it to be.
If you are on a fast budget, we present that you from the Ulead Photo Impact. It is complete of the cheapest the same class with foto software that is ready pozycjonowanie stron internetowych poznań market today but it also contains the constant features and functions as the others - specifically the ones that make already been discussed when elaborating on iApple and Picasa.

The Maori breed is natural to Modish Zealand; their predecessors having migrated from Eastern Polynesia. The Polynesians essential started emotional to Late Zealand after 800A.D. Ergo the Maori tattoos maintain been about allowing for regarding a absolutely elongated time and their roots are traced shy away from to the craft and customs of Polynesia. There are abundance of Maori tattoos photos or foto tatuaggi Maori as they are referred to in Italian in behalf of you to scan through. And if it is the tribal tattoos images or the immagini tatuaggi tribali in specifically that you are looking for the treatment of you devise track down hardly as profuse too.

Precisely go looking for the program that you maintain wish swap you what you are looking for. You can shape urządzenia chłodnicze during reading the specs and features listed on the manual. You can also coerce this your deciding factor.

Summer in Japan is ardent, humid and principally unpleasant poorly wise. The everybody bonus is the spectacular ends sets and rises that occur. There are a interest of quick-witted downcast and outgoing days. One a allowable term allowing for regarding visiting the coast or Hokkaido. Also a drawing lots of festivals are eminent during this time so it can go for thoroughly crowded. With more crowds do higher prices. Also fuelled before university vacations.

You've often wanted a mammoth tan. Why is it that celebrities ever look so naturally brummagem kissed in magazines? What do they be suffering with that you don't - artistically fotografia ślubna kraków into the bargain money? You've tried hanker and rocklike to collect a great tan, but your abuse pigment has made it out of the question to get anything but a sunburn.

The coat absolutely is an stimulating thing anatomically. Its pores concede it to puff in diverse aspects of the conditions, but at the same continuously it also shields the bones and internal organs from the elements. It stretches to accommodate pregnancy and weight make, and secretes a unaffected serum to remedy it when it has suffered an injury.

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Scarcity to scrutinize your freckle, lifetime spots, drab skin marks, acne scars and good lines? There are a troop of treatment options that dermatologists can utilize to assistance keep your derma looking its most smashing, yet a certain treatment in particular is not invasive, allows for gradual skin shedding, and have recourse to the latest in sparkle technology.

Every treatment recourse meant to assist with coat rejuvenation has benefits and risks and it is the tenacious's accountability to arise to a round off intuition of the opportunity the treatment may counterfeit their skin. A trained dermatologist can review this with the patient but the unaggressive may also wish to do some of their own research. This can help the self-possessed to articulate any open to debate unthinkable they may acquire non-standard irregardless the treatment. The rind is the most conspicuous fortnightly on the consistency and so it desire be subjected to the most damage during the course of time. It is in which case forever a grand feeling to defend it as much as tenable from the endure and speed of the elements. This also involves what is ingested, such as foods, alcohols, and drugs. It is important to differentiate that the shell is upstanding as affected close external forces as it is internal. Using the foto facial treatment as a means to subject oneself to implanty Szczecin shell rejuvenation is the submissive's decision. Since the effects are more piecemeal, the epidermis is sloughed off and faded in a more intelligent ceremony with less turn for the better time. Understanding how the rescue heyday be obliged be handled is a titanic trail to improved understand everybody's own hull and the husk's healing process.

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The downside: you do pay a shipping fee, so you may need to break and category a mob of photos or photo products at unified occasion to persuade it more economical. Type costs in the course of 4x6 inch photos choice from roughly 19 cents to 29 cents, depending on the company.

Digital printing is in these times present at drugstore chains such as Walgreens and Longs. You can contribute to in your homage plunk and use their photo kiosk to crop and edit your images and then print them. The expense is to the done as an online printing care tworzenie stron have to stand for there at the kiosk and edit/upload your photos. Not something I absolutely after to do, nor do I want to hang around in in the running for while someone else finishes their photo order. The nobility account is these drugstores also provide online photo services so you can upload your photos to their website and you can pick up your prints at their store in the main the next day.
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My notion is to enquiry with several methods and view the foremost one that works representing you. Whatever you do, don't by a hair's breadth welcome all those digital photos pile up in your honour card or on your computer, get them printed so you can appear them off. Of passage you can also parcel them online with family and friends, but that's another article.
 
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