Question

Срочноооо!!!!! Обчислити значення виразу

якщо p = 49, q = 25.

Answer 1

$\displaystyle\bf\\\Big(\dfrac{\sqrt{q} }{p-\sqrt{pq} } +\dfrac{\sqrt{p} }{q-\sqrt{pq} } \Big)\cdot\dfrac{p\sqrt{q} +q\sqrt{p} }{p-q} =\\\\\\=\Big(\dfrac{\sqrt{q} }{(\sqrt{p} )^{2} -\sqrt{pq} } +\dfrac{\sqrt{p} }{(\sqrt{q} )^{2} -\sqrt{pq} } \Big)\cdot\dfrac{p\sqrt{q} +q\sqrt{p} }{(\sqrt{p})^{2} -(\sqrt{q} )^{2} } =$

$\displaystyle\bf\\=\Big(\dfrac{\sqrt{q} }{\sqrt{p}(\sqrt{p} -\sqrt{q}) } +\dfrac{\sqrt{p} }{\sqrt{q} (\sqrt{q} -\sqrt{p}) } \Big)\cdot\dfrac{\sqrt{pq} (\sqrt{p} +\sqrt{q} )}{(\sqrt{p} -\sqrt{q} )(\sqrt{p} +\sqrt{q} )} =\\\\\\=\dfrac{\sqrt{q} \cdot\sqrt{q} -\sqrt{p}\cdot\sqrt{p}}{\sqrt{pq} (\sqrt{p} -\sqrt{q} )} \cdot\dfrac{\sqrt{pq} }{\sqrt{p} -\sqrt{q} } =\dfrac{q-p}{(\sqrt{p} -\sqrt{q} )^{2} } =\dfrac{\sqrt{q} +\sqrt{p} }{\sqrt{q} -\sqrt{p} } \\\\\\p=49 \ ; \ q=25$

$\displaystyle\bf\\\dfrac{\sqrt{q} +\sqrt{p} }{\sqrt{q} -\sqrt{p} } =\dfrac{\sqrt{25} +\sqrt{49} }{\sqrt{25} -\sqrt{49} } =\dfrac{5+7}{5-7} =\dfrac{12}{-2} =\boxed {-6}$