Question

Se considera numarul real a=√5-2√6+√5+2√6.Aratati ca a²=12 (radicalul de la 5esta cu tot cu2√6)deci radicalele de langa 5 sunt mari)

Answer 1

a²=($\sqrt{5-2 \sqrt{6} }+ \sqrt{5+2 \sqrt{6} }$)²
= 5-2√6+5+2√6+2$\sqrt{(5-2 \sqrt{6} )(5+2 \sqrt{6} )}$
=10+2$\sqrt{ 5^{2}- (2 \sqrt{6}) ^{2} }$= 10+2$\sqrt{25-24}$=10+2=12