Question

Se considera numarul real a= $\sqrt{5-2 \sqrt{} 6}$+$\sqrt{5+2 \sqrt{} 6}$ .Aratati ca $a^{2}$=12 .

Answer 1

Folosim formula  a²+b²=a²+2ab+b² , unde 
a=$\sqrt{5-2 \sqrt{6} }$
b=$\sqrt{5+2 \sqrt{6} }$
a²=$5-2 \sqrt{6}$+2$\sqrt{(5-2 \sqrt{6)}(5+2 \sqrt{6} )} }$+$5+2 \sqrt{6}$
Folosind formula  a²-b²=(a-b)(a+b) relatia devine
a²=10+2$\sqrt{25-24}$
a²=10+2
a=12