Giúp tớ với!!!

M

maihoc98

bài 3 nhé
a^2+b^2+c^2= ab+ac+bc
\Rightarrow2a^2+2b^2+2c^2=2ab+2ac+2bc
\Rightarrow2a^2+2b^2+2c^2-2ab-2bc-2ac=0
\Rightarrow(a^2-2ab+b^2)+(a^2-2ac+c^2)+(b^2-2bc+c^2)=0
(a-b)^2+(a-c)^2+(b-c)^2=0
Vì (a-b)^2\geq 0 vs mọi a,b
(a-c)^2\geq 0 vs mọi a,c
(b-c)^2\geq 0 vs mọi b,c
Do đó (a-b)^2+(b-c)^2+(b-c)^2=0khi a-b=a-c=b-c=0
\Rightarrowa=b=c(đpcm)
thanks m đi ha đuung 100%
 
G

g_dragon88

Nhớ ấn nút thank nha!

Bài 1: Ta có: ([TEX] a^2[/TEX]+[TEX] b^2[/TEX])([TEX] x^2[/TEX]+[TEX] y^2[/TEX]) = [TEX] (ax+by)^2[/TEX]
\Leftrightarrow [TEX] a^2[/TEX][TEX] x^2[/TEX]+[TEX] a^2[/TEX][TEX] y^2[/TEX]+[TEX] b^2[/TEX][TEX] x^2[/TEX]+[TEX] b^2[/TEX][TEX] y^2[/TEX]=[TEX] a^2[/TEX][TEX] x^2[/TEX]+ 2axby + [TEX] b^2[/TEX][TEX] y^2[/TEX]
\Leftrightarrow [TEX] a^2[/TEX][TEX] x^2[/TEX]+[TEX] a^2[/TEX][TEX] y^2[/TEX]+[TEX] b^2[/TEX][TEX] x^2[/TEX]+[TEX] b^2[/TEX][TEX] y^2[/TEX] - [TEX] a^2[/TEX][TEX] x^2[/TEX]- 2axby - [TEX] b^2[/TEX][TEX] y^2[/TEX]=0
\Leftrightarrow
[TEX] a^2[/TEX][TEX] y^2[/TEX] - 2axby+[TEX] b^2[/TEX][TEX] x^2[/TEX]=0
\Rightarrow [TEX] (ay-bx)^2[/TEX]=0
\Rightarrow ay = bx
\Rightarrow dpcm
 
G

g_dragon88

Nhớ ấn nút thank nha!

Bài 2:Ta có: a+b+c = 2p
\Rightarrow a+b+c-2a = 2p-2a
\Rightarrow b+c-a= 2(p-a)
\Rightarrow (b+c+a)(b+c-a)=2p.2(p-a)
\Rightarrow [TEX] (b+c)^2[/TEX]-[TEX] a^2[/TEX]= 4p(p-a)
\Rightarrow [TEX] b^2[/TEX]+[TEX] c^2[/TEX]+2bc - [TEX] a^2[/TEX]= 4p.(p-a)
\Rightarrow dpcm
 
G

g_dragon88

Bài 3 thì ''maihoc98'' làm đúng rồi..............................................................
 
P

phong_1998

Bài 2: CMR: Nếu a+b+c=2p thì b^2+c^2+2bc-a^2= 4p.(p-a)

b^2+c^2+2bc-a^2=(b+c)^2-a^2=(a+b+c)*(b+c-a)
ma a+b+c=2p\Rightarrowb^2+c^2+2bc-a^2=2p*(2p-2a)=4p*(p-a)
 
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