Question

Cho biểu thức : P = \(\dfrac{x}{\left(\sqrt{x}+\sqrt{y}\right)\left(1-\sqrt{y}\right)}\) - \(\dfrac{y}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}+1\right)}\) - \(\dfrac{xy}{\left(\sqrt{x}+1\right)\left(1-\sqrt{y}\right)}\)

Tính giá trị x;y nguyên thỏa mãn P= 2

Answer 1

\(P=\frac{x}{\left(\sqrt{x}+\sqrt{y}\right)\left(1-\sqrt{y}\right)}-\frac{y}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}+1\right)}-\frac{xy}{\left(\sqrt{x}+1\right)\left(1-\sqrt{y}\right)}\)

\(=\sqrt{xy}+\sqrt{x}-\sqrt{y}\)

\(P=2\Rightarrow\sqrt{xy}+\sqrt{x}-\sqrt{y}=2\)

\(\Rightarrow\left[{}\begin{matrix}x=y=2\\x=4;y=0\end{matrix}\right.\) (t/m)