Question

Решите задачу пожалуйста: (2/(√19+√17 )+ 2/(√17+√15 )+√15) * √19

Answer 1

$\frac{2}{ \sqrt{19}+ \sqrt{17} }= \frac{2(\sqrt{19}- \sqrt{17})}{(\sqrt{19}+ \sqrt{17})(\sqrt{19}- \sqrt{17} )}= \\ \\ = \frac{2(\sqrt{19}- \sqrt{17})}{(\sqrt{19}) ^{2} -( \sqrt{17}) ^{2} }= \frac{2(\sqrt{19}- \sqrt{17})}{2 }=\sqrt{19} - \sqrt{17}$
$\frac{2}{ \sqrt{17}+ \sqrt{15} }= \frac{2(\sqrt{17}- \sqrt{15})}{(\sqrt{17}+ \sqrt{15})(\sqrt{17}- \sqrt{15} )}= \\ \\ = \frac{2(\sqrt{17}- \sqrt{15})}{(\sqrt{17}) ^{2} -( \sqrt{15}) ^{2} }=\frac{2(\sqrt{17}- \sqrt{15})}{2}=\sqrt{17} - \sqrt{15}$
$(\sqrt{19} - \sqrt{17}+\sqrt{17} - \sqrt{15}+ \sqrt{15})\cdot \sqrt{19}=19$