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. HEEEEEELLLLLLLLPPPPPPPPPPP

Answer 1

[tex]\it a = \dfrac{2}{3+\sqrt{11}} = \dfrac{2}{\sqrt{11} +3} = \dfrac{2(\sqrt{11}-3)}{11-9} = \dfrac{2(\sqrt{11}-3)}{2} =\sqrt{11}-3 \\\;\\ \\\;\\ \sqrt{5\dfrac{1}{2}} = \sqrt{\dfrac{11}{2}} = \dfrac{\sqrt{11}}{\sqrt2}[/tex]

[tex]\it b = 3+\sqrt2\cdot\dfrac{\sqrt{11}}{\sqrt2} = 3+\sqrt{11} =\sqrt{11}+3 \\\;\\ \\\;\\ m_a = \dfrac{a+b}{2} =\dfrac{\sqrt{11}-3+\sqrt{11}+3}{2} = \dfrac{2\sqrt{11}}{2}=\sqrt{11} [/tex]