Question

a) Rút gọn biểu thức: $A=\sqrt{28}+\sqrt{63}-2 \sqrt{7}$
b) Chứng minh rằng: $\dfrac{x \sqrt{y}+y \sqrt{x}}{\sqrt{x y}}: \dfrac{1}{\sqrt{x}-\sqrt{y}}=x-y$ với $x>0 ; y>0 ; x \neq y$

Answer 1

a) \(A=2\sqrt{7}+3\sqrt{7}-2\sqrt{7}\\ A=3\sqrt{7}\)

b) \(\Leftrightarrow\dfrac{\left(x\sqrt{y}+y\sqrt{x}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}=x-y\\ \dfrac{x\sqrt{xy}+xy-xy-y\sqrt{xy}}{\sqrt{xy}}=x-y\\ \dfrac{x\sqrt{xy}-y\sqrt{xy}}{\sqrt{xy}}=x-y\\ x-y=x-y\)

 

Answer 2

a) \(A=2\sqrt{7}+3\sqrt{7}-2\sqrt{7}\\ A=3\sqrt{7}\)

b) \(\Leftrightarrow\dfrac{\left(x\sqrt{y}+y\sqrt{x}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}=x-y\\ \dfrac{x\sqrt{xy}+xy-xy-y\sqrt{xy}}{\sqrt{xy}}=x-y\\ \dfrac{x\sqrt{xy}-y\sqrt{xy}}{\sqrt{xy}}=x-y\\ x-y=x-y\)