Question

1,cho pt P=\(\dfrac{(\sqrt{x}-\sqrt{y})^2-4\sqrt{xy}}{\sqrt{x}+\sqrt{y}}-\dfrac{x\sqrt{y}-y\sqrt{x}}{\sqrt{xy}}\)

a, tìm ĐKXĐ và rút gọn P

b, tìm giá trị của P khi y=4-2\(\sqrt{3}\)

Answer 1

Lời giải:

a) ĐK: \(x>0; y> 0\)

\(P=\frac{(\sqrt{x}-\sqrt{y})^2+4\sqrt{xy}}{\sqrt{x}+\sqrt{y}}-\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{xy}}\)

\(=\frac{x-2\sqrt{xy}+y+4\sqrt{xy}}{\sqrt{x}+\sqrt{y}}-\frac{\sqrt{xy}(\sqrt{x}-\sqrt{y})}{\sqrt{xy}}\)

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

\(=\frac{(\sqrt{x}+\sqrt{y})^2}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}-\sqrt{y})=(\sqrt{x}+\sqrt{y})-(\sqrt{x}-\sqrt{y})=2\sqrt{y}\)

b)

Khi \(y=4-2\sqrt{3}=3+1-2\sqrt{3.1}=(\sqrt{3}-1)^2\)

\(\Rightarrow \sqrt{y}=\sqrt{3}-1\)

\(\Rightarrow P=2\sqrt{y}=2(\sqrt{3}-1)\)