Question

Puteti sa imi rezolvati si mie? (imagine)

Answer 1

$\sqrt{11- \sqrt{21} } = \sqrt{ \frac{11+ \sqrt{121-21} }{2} } - \sqrt{ \frac{11- \sqrt{121-21} }{2} } = \sqrt{ \frac{11+10}{2} } - \sqrt{ \frac{11-10}{2} }$
$\frac{ \sqrt{21} }{ \sqrt{2} } - \frac{ \sqrt{1} }{ \sqrt{2} } = \frac{ \sqrt{42} }{2} - \frac{ \sqrt{2} }{2} = \frac{ \sqrt{42} - \sqrt{2} }{2}$
Cealalta expresie este la fel, doar ca e cu plus intre termeni :
$\frac{ \sqrt{42} + \sqrt{ \sqrt{2} } }{2}$
$a= \frac{ \sqrt{42} - \sqrt{2} }{2} - \frac{ \sqrt{42} + \sqrt{2} }{2} = \frac{ \sqrt{42} - \sqrt{2} - \sqrt{42} - \sqrt{2} }{2} =- \frac{2 \sqrt{2} }{2} =- \sqrt{2}$
$(- \sqrt{2} + \sqrt{2} -1) ^{2016}=(-1) ^{2016} =1$