Question

Se considera numerele a=2 supra 3+radical din 11 si b=3+radical din 2* radical din 5 intregi si 1 pe 2.Calculati media aritmetica a celor doua numere. ajutoor!

Answer 1

$\displaystyle a=\frac{2}{3}+\sqrt{11}=\frac{2+3\sqrt{11}}{3} \\ b=3+\sqrt2\times\sqrt5\frac{1}{2}=3+\sqrt2\times\frac{2\sqrt5+1}{2}=3+\frac{2\sqrt{10}+\sqrt2}{2}=\frac{6+2\sqrt{10}+\sqrt2}{2} \\ m_a=\frac{a+b}{2} \\ m_a=\frac{\frac{2+3\sqrt{11}}{3}+\frac{6+2\sqrt{10}+\sqrt2}{2}}{2}=\frac{4+6\sqrt{11}+18+6\sqrt{10}+3\sqrt2}{12}= \\ \frac{22+6(\sqrt{11}+\sqrt{10})+3\sqrt2}{2}$