Question

GPT sau: \(x+\sqrt{17-x^2}+x\sqrt{17-x^2}=9\)

Answer 1

ĐKXĐ: ...

Đặt \(\left\{{}\begin{matrix}u=v\\v=\sqrt{17-x^2}\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}u+v+uv=9\\u^2+v^2=17\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}uv=9-\left(u+v\right)\\\left(u+v\right)^2-2uv=17\end{matrix}\right.\)

\(\Rightarrow\left(u+v\right)^2+2\left(u+v\right)-35=0\)

\(\Rightarrow\left[{}\begin{matrix}u+v=5\Rightarrow uv=4\\u+v=-7\Rightarrow uv=16\end{matrix}\right.\)

\(\Rightarrow...\)