The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that

Question

Philoid · Accepted Answer

Here, the two numbers are a and b.

Arithmetic Mean = AM = (a + b)/2

& Geometric Mean = GM = √(ab)

According to question -

Applying component dividend

Applying Component Dividend

Squaring both sides

Hence, Proved.