Hệ phương trình \(\left\{\begin{array}{l} 3 \sqrt{x-1}+2 \sqrt{y}=13 \\ 2 \sqrt{x-1}-\sqrt{y}=4 \end{array}\right.\) có nghiệm là:

* Hướng dẫn giải

 \(\begin{aligned} &\text { Điều kiện: } x \geq 1 ; y \geq 0\\ &\text { Ta có }\left\{\begin{array}{l} 3 \sqrt{x-1}+2 \sqrt{y}=13 \\ 2 \sqrt{x-1}-\sqrt{y}=4 \end{array} \Leftrightarrow\left\{\begin{array}{l} 3 \sqrt{x-1}+2 \sqrt{y}=13 \\ 4 \sqrt{x-1}-2 \sqrt{y}=8 \end{array} \Leftrightarrow\left\{\begin{array}{l} 2 \sqrt{x-1}-\sqrt{y}=4 \\ 7 \sqrt{x-1}=21 \end{array}\right.\right.\right.\\ &\Leftrightarrow\left\{\begin{array}{l} \sqrt{x-1}=3 \\ 3.3+2 \sqrt{y}=13 \end{array} \Leftrightarrow\left\{\begin{array}{l} x-1=9 \\ 2 \sqrt{y}=4 \end{array} \Leftrightarrow\left\{\begin{array}{l} x=10 \\ y=4 \end{array}(\text { thỏa mãn })\right.\right.\right. \end{aligned}\)