Question

Which of the following is true if A means arithmetic mean and b means geometric mean of two numbers?

(a) A>G

(b) A≥G

(c) G<A

(d) G≤A

I have been asked this question by my school principal while I was bunking the class.

I need to ask this question from Relationship Between A.M. and G.M. topic in division Sequences and Series of Mathematics – Class 11

Answer 1

The correct option is (b) A≥G

Easiest explanation: We know, A.M. of two numbers a and b is (a + b)/2

Also, G.M. of two numbers a and b is \(\sqrt{ab}\)

A-G = (a + b)/2 – \(\sqrt{ab} = ((a + b) – 2\sqrt{ab})/2 = (\sqrt{a} – \sqrt{b})^2\) / 2 ≥ 0

So, A≥G.