Question

Giúp mình với

Answer 1

\(M.1011^2=\dfrac{1011^2}{x^2+1011^2}+\dfrac{1011^2}{y^2+1011^2}=1-\dfrac{x^2}{x^2+1011^2}+1-\dfrac{y^2}{y^2+1011^2}\)

\(\ge1-\dfrac{x^2}{2.1011x}+1-\dfrac{y^2}{2.1011y}=2-\dfrac{1}{2022}\left(x+y\right)=2-1=1\)

\(\Rightarrow M\ge\dfrac{1}{1011^2}\)

Dấu "=" xảy ra khi \(x=y=1011\)