tìm Min

H

hoang_duythanh

y=(0,5−x)2+(0,75)2+(0,5+x)2+(0,75)2\sqrt[]{(0,5-x)^2+(\sqrt[]{0,75})^2}+\sqrt[]{(0,5+x)^2+(\sqrt[]{0,75})^2}
Áp dụng a2+b2+c2+d2\sqrt[]{a^2+b^2}+\sqrt[]{c^2+d^2}\geq(a+c)2+(b+d)2\sqrt[]{(a+c)^2+(b+d)^2} ..cái này muốn cm chỉ cần bình phương lên ,rút gọn ra dc (ad−bc)2(ad-bc)^2\geq0.Dấu = xảy ra khi ad=bc
=>y \geq 2 .
Dấu = xảy ra khi .........
 
G

gf_braga

y=x2−x+1+x2+x+1=(12−x)2+(32)2+y=\sqrt{x^2-x+1}+\sqrt{x^2+x+1}=\sqrt{\left(\dfrac{1}{2}-x\right)^2+\left(\dfrac{\sqrt{3}}{2}\right)^2}+ (x+12)2+(32)2\sqrt{\left(x+\dfrac{1}{2}\right)^2+\left(\dfrac{\sqrt{3}}{2}\right)^2}
Theo MinkovskyMinkovsky thì:
y≥(12−x+x+12)2+(32+32)2=4=2y\ge \sqrt{\left(\dfrac{1}{2}-x+x+\dfrac{1}{2}\right)^2+\left(\dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{3}}{2}\right)^2}=\sqrt{4}=2
 
You must log in or register to reply here.
Top Bottom