Question

Calculati media aritmetica a numerelor: (√2+√3)² si (√6-1)². sa imi scrie-ti va rog rezolvarea completa.

Answer 1

$( \sqrt{2} + \sqrt{3} )^{2}= ( \sqrt{2} )^{2}+2* \sqrt{2} * \sqrt{3} + ( \sqrt{3} )^{2} =2+2* \sqrt{6} +3=5+2* \sqrt{6}$
$( \sqrt{6}-1 )^{2}= ( \sqrt{6} )^{2} -2* \sqrt{6} *1+ 1^{2} =6-2* \sqrt{6} +1=7-2* \sqrt{6}$
Media aritmetica are formula: $medaritm= \frac{a+b}{2}$, iar la noi $a=( \sqrt{2} + \sqrt{3} )^{2}$ si $b=( \sqrt{6}-1 )^{2}$.
Deci $medaritm= \frac{5+2 \sqrt{6}+7-2\sqrt{6} }{2} = \frac{12}{2} =6$