Question

Valoarea raportului a doua numere naturale este 1/3 , iar media lor aritmetica este 36 . Calculati media geometrica a celor doua numere.

Answer 1

$\frac{a}{b}= \frac{1}{3} \\ \\ \frac{a}{1}=\frac{b}{3}=k \\ a=k \\ b=3k \\ \\ ma= \frac{a+b}{2}= \frac{k+3k}{2}= \frac{4k}{2}= 2k \\ \\ma=36 \\ 36=2k => \boxed{k=18} \\ \\ a=k => \boxed{a=18} \\ \\ b=3k=> \boxed{b=54} \\ \\ mg= \sqrt{ab} = \sqrt{18*54} \\ \\ mg= \sqrt{972} =18 \sqrt{3}$

Answer 2

$\frac{a}{b} = \frac{1}{3}$ =>  b=3a
(3a+a)/2=36
4a/2=36
2a=36
a=18
b=3a, b=3x18, b=54

mg = $\sqrt{ab} = \sqrt{18*54} = \sqrt{972} = 18 \sqrt{3}$