Question

$a = \sqrt{4 - \sqrt{15 } } + \sqrt{4 + \sqrt{15} }$
Ma poate ajuta cineva? va rog​

Answer 1

 

$\displaystyle\bf\\a=\sqrt{4-\sqrt{15}}+\sqrt{4+\sqrt{15}}~~\Big|~(ridicam~la~patrat)\\\\\\a^2=\left(\sqrt{4-\sqrt{15}}+\sqrt{4+\sqrt{15}}\right)^2\\\\\\a^2=\left(\sqrt{4-\sqrt{15}}\right)^2+\left(\sqrt{4+\sqrt{15}}\right)^2+2\left(\sqrt{4-\sqrt{15}}\right)\left(\sqrt{4+\sqrt{15}}\right)$

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$\displaystyle\bf\\a^2=4-\sqrt{15}+4+\sqrt{15}+2\sqrt{\Big(4-\sqrt{15}\Big)\Big(4+\sqrt{15}\Big)}\\\\\\a^2=4+4\underbrace{-\sqrt{15}+\sqrt{15}}_{=~0}+2\sqrt{4^2-\Big(\sqrt{15}\Big)^2} \\\\\\a^2=4+4+2\sqrt{16-15}\\\\a^2=8+2\sqrt{1}\\\\a^2=8+2\\\\a^2=10\\\\\boxed{\bf a=\sqrt{10}}$