Question

Giải hệ phưng trình \(\left\{{}\begin{matrix}\sqrt{x-1}+2\sqrt{y}=5\\\frac{4x-9y-4}{2\sqrt{x-1}+3\sqrt{y}}=-4\end{matrix}\right.\)

Answer 1

ĐK : \(x\ge-1;y\ge0\)

Ta có HPT : \(\left\{{}\begin{matrix}\sqrt{x-1}+2\sqrt{y}=5\left(1\right)\\\frac{4x-9-y}{2\sqrt{x-1}+3\sqrt{y}}=-4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2\sqrt{x-1}+4\sqrt{y}=10\\2\sqrt{x-1}-3\sqrt{y}=-4\end{matrix}\right.\)

\(\Rightarrow7\sqrt{y}=14\) \(\Leftrightarrow y=4\)

Thay y = 4 vào ( 1 ) , ta được : \(\sqrt{x-1}+2\sqrt{y}=5\)

\(\Leftrightarrow\sqrt{x-1}+4=5\) \(\Leftrightarrow x-1=1\Leftrightarrow x=2\)

Vậy ...