Question

x²= 8+2√7

Help

Trebuie ca x sa aparțină numerelor reale

Answer 1

$x= \sqrt{8+2 \sqrt{7} }$

$x= \sqrt{8+ \sqrt{28} }$

Avem formula:

$x= \sqrt{a+ \sqrt{b} }= \sqrt{ \frac{a+c}{2} } + \sqrt{ \frac{a-c}{2} }$

$c= \sqrt{ a^{2}-b }$

$c= \sqrt{8^{2}-28 }= \sqrt{64-28}= \sqrt{36}=6$

$x= \sqrt{ \frac{8+6}{2} }+ \sqrt{ \frac{8-6}{2} }= \sqrt{ \frac{14}{2} }+ \sqrt{ \frac{2}{2} }= \sqrt{7}+ \sqrt{1}= \sqrt{7}+1$

$x= \left[\begin{array}{ccc} \sqrt{7}+1 \end{array}\right]$