Question

Biết x, y thỏa mãn \(2x^2+\dfrac{1}{x^2}+\dfrac{y^2}{4}=4\). Tính max A=x.y

Answer 1

\(2x^2+\dfrac{1}{x^2}+\dfrac{y^2}{4}=4\)

\(\Leftrightarrow\left(x-\dfrac{1}{x}\right)^2+\left(x-\dfrac{y}{2}\right)^2=2-xy\)

\(\Rightarrow2-xy\ge0\)

\(\Rightarrow xy\le2\)

\(A_{max}=2\) khi \(\left(x;y\right)=\left(1;2\right);\left(-1;-2\right)\)