Монгол Бодлогын Сан

Заавар: $\sqrt{x}=a$, $\sqrt{y}=b$ орлуулга ашигла.

Бодолт: $\sqrt{x}=a$, $\sqrt{y}=b$ гэвэл $$\begin{align*} \text{Илэрх.}&=\biggl(\sqrt x-\frac{\sqrt{xy}+y}{\sqrt x+\sqrt y}\biggr)\cdot \biggl(\frac{\sqrt x}{\sqrt x+\sqrt y}+\frac{\sqrt y}{\sqrt x-\sqrt y}+\frac{2\sqrt {xy}}{x-y}\biggr)\\ &=\biggl(a-\frac{b(a+b)}{a+b}\biggr)\cdot \biggl(\frac{a}{a+b}^{\color{red}{(a-b}}+\frac{b}{a-b}^{\color{red}{(a+b}}+\frac{2ab}{a^2-b^2}\biggr)\\ &=(a-b)\cdot\dfrac{a^2-ab+ba+b^2+2ab}{(a-b)(a+b)}\\ &=\dfrac{a^2+2ab+b^2}{a+b}=\dfrac{(a+b)^2}{a+b}\\ &=a+b=\sqrt x+\sqrt y \end{align*}$$