Question

If a and g are the
a.M and g.M between any two distinct positive number a and b then shown that a>g

Answer 1

Step-by-step explanation:

A.M. and G.M. between a and b are a and g respectively.

So,

a= 1/2(a+b)

g= √(ab)

a-g = 1/2(a+b)-√(ab)

= 1/2 {(a+b) - 2√(ab)}

=1/2 {(√a)² + (√b)² - 2√a√b}

= 1/2 (√a - √b)² > 0 [since, a and b are positive number and (√a - √b)² > 0 ]

therefore, a-g > 0 => a > g

Proven