tìm Min

H

hoang_duythanh

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

gf_braga

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