Монгол Бодлогын Сан

Заавар: $a^{0.5}=x$, $b^{0.5}=y$ орлуулга ашигла.

Бодолт: $a^{0.5}=x$, $b^{0.5}=y$ орлуулбал: $$\begin{align*} \text{Илэрх.}&=\biggl(\dfrac{2}{a^{0.5}-b^{0.5}}-\dfrac{2a^{0.5}}{a^{1.5}+b^{1.5}}\cdot\dfrac{a-a^{0.5}b^{0.5}+b}{a^{0.5}-b^{0.5}}\biggr): \dfrac{4a^{0.5}b^{0.5}}{a-b}\\ &=\biggl(\dfrac{2}{x-y}-\dfrac{2x}{x^3+y^3}\cdot\dfrac{x^2-xy+y^2}{x-y}\biggr):\dfrac{4xy}{x^2-y^2}\\ &=\biggl(\dfrac{2^{\color{WildStrawberry}{(x+y}}}{x-y}-\dfrac{2x}{(x+y)(x^2-xy+y^2)}\cdot\dfrac{x^2-xy+y^2}{x-y}\biggr):\dfrac{4xy}{x^2-y^2}\\ &=\biggl(\dfrac{2x+2y}{x^2-y^2}-\dfrac{2x}{x^2-y^2}\biggr):\dfrac{4xy}{x^2-y^2}\\ &=\dfrac{2y}{x^2-y^2}:\dfrac{4xy}{x^2-y^2}\\ &=\dfrac{2y}{x^2-y^2}\cdot\dfrac{x^2-y^2}{4xy}\\ &=\dfrac{1}{2x}=\dfrac{1}{2a^{0.5}}=\dfrac12a^{-0.5} \end{align*}$$