Question

tìm x,y 

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

giải hộ mk nhé

Answer 1

Ta có: \(x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=4\)

\(\Leftrightarrow\left(x^2+\frac{1}{x^2}-2\right)+\left(y^2-2+\frac{1}{y^2}\right)=0\)

\(\Leftrightarrow\left(x-\frac{1}{x}\right)^2+\left(y-\frac{1}{y}\right)^2=0\)

\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{x}\\y=\frac{1}{y}\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x^2=1\\y^2=1\end{cases}}\)

\(\Leftrightarrow\)(x, y) = (1, 1; 1, - 1; - 1, 1; - 1, - 1)