Question

Calculati media aritmetica si media geometrica a numerelor reale x=2/√7+√6 si y=√28+√24
Plssss

Answer 1

Răspuns:

Explicație pas cu pas:

$x=\frac{2}{\sqrt{7} +\sqrt{6} }=\frac{2*(\sqrt{7} -\sqrt{6})}{(\sqrt{7} +\sqrt{6})(\sqrt{7} -\sqrt{6})}=\frac{2*(\sqrt{7} -\sqrt{6})}{(\sqrt{7})^{2}-(\sqrt{6})^{2}}=\frac{2*(\sqrt{7} -\sqrt{6})}{7-6} =2*(\sqrt{7} -\sqrt{6}) \\y=\sqrt{28} +\sqrt{24}=\sqrt{4*7} +\sqrt{4*6} =2*\sqrt{7}+2*\sqrt{6}=2*(\sqrt{7} +\sqrt{6}).\\ma=\frac{x+y}{2}=\frac{2*(\sqrt{7} -\sqrt{6})+2*(\sqrt{7} +\sqrt{6})}{2}=\frac{2*(\sqrt{7} -\sqrt{6}+\sqrt{7} +\sqrt{6} ) }{2} =2*\sqrt{7}.$

$mg=\sqrt{x*y}=\sqrt{2*(\sqrt{7} -\sqrt{6})*2*(\sqrt{7} +\sqrt{6})} =\sqrt{4*(\sqrt{7} -\sqrt{6})*(\sqrt{7} +\sqrt{6})} =2*\sqrt{(\sqrt{7})^{2}-(\sqrt{6})^{2}} =2*\sqrt{7-6}=2*\sqrt{1}=2*1=2.$