Question

Помогите пожалуйста,срочно надо.Заранее спасибо))))

Answer 1

$\displaystyle\bigg(\frac{\sqrt{q}}{p-\sqrt{pq}}+\frac{\sqrt{p}}{q-\sqrt{pq}}\bigg)\cdot\frac{p\sqrt{q}+q\sqrt{p}}{p-q}=\\\\\\=\bigg(\frac{\sqrt{q}}{\sqrt{p}(\sqrt{p}-\sqrt{q})}-\frac{\sqrt{p}}{\sqrt{q}(\sqrt{p}-\sqrt{q})}\bigg)\cdot\frac{\sqrt{pq}(\sqrt{p}+\sqrt{q})}{(\sqrt{p}-\sqrt{q})(\sqrt{p}+\sqrt{q})}=\\\\\\=\frac{q-p}{\sqrt{pq}(\sqrt{p}-\sqrt{q})} \cdot\frac{\sqrt{pq}}{\sqrt{p}-\sqrt{q}}=\frac{(\sqrt{q}-\sqrt{p})(\sqrt{q}+\sqrt{p})}{(\sqrt{q}-\sqrt{p})^2}=\frac{\sqrt{q}+\sqrt{p}}{\sqrt{q}-\sqrt{p}}$

если р = 81; q = 100:

$\displaystyle\frac{\sqrt{q}+\sqrt{p}}{\sqrt{q}-\sqrt{p}}=\tt\frac{\sqrt{100}+\sqrt{81}}{\sqrt{100}-\sqrt{81}}=\frac{10+9}{10-9}=\frac{19}{1}$