Question

(1/3-2X)^2020+(3Y-X)^2022 lớn hơn hoặc bằng 0 chứng minh 1/x+1/y=24

giúp mk với ah

Answer 1

Sửa: \(\left(\dfrac{1}{3}-2x\right)^{2020}+\left(3y-x\right)^{2022}\le0\)

Mà \(\left(\dfrac{1}{3}-2x\right)^{2020}+\left(3y-x\right)^{2022}\ge0\) với mọi x,y

Do đó \(\left\{{}\begin{matrix}\dfrac{1}{3}-2x=0\\3y-x=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{6}\\y=\dfrac{1}{18}\end{matrix}\right.\)

\(\Leftrightarrow\dfrac{1}{x}+\dfrac{1}{y}=6+18=24\)