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Prove that a.p. is greater than g.p of two numbers. If they are greater than 0

Prove that a.p. is greater than g.p of two numbers. If they are greater than 0

Grade:10

2 Answers

Shailendra Kumar Sharma
188 Points
4 years ago
Assume a, and b
AM-GM will be
(a+b)/2-\sqrt{ab} 
(a+b-2\sqrt{ab})/2
(\sqrt{a } -\sqrt{b})^{2}/2  which is always greater than or equal to zero thus AM is always more than gm
Namit Vijaivergia
11 Points
4 years ago
Let a, b be two numbers greater than 0. And a>ba-b>0Squaring both sides(a-b)^2>0Adding 4ab to both sides (a+b)^2>2abSquare rooting both sides(a+b)÷2>(ab)^.5A.M>G.m

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