Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 2008-03-30 17:31:28

Identity
Member
Registered: 2007-04-18
Posts: 934

Inequality! Yay!

Prove that for all reals

,
.

I've tried at this one for ages, but it's probably beyond me... anyway, give it a shot!

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#2 2008-03-30 21:42:10

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Inequality! Yay!

By the Cauchy–Schwarz inequality

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#3 2008-03-30 22:52:58

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Inequality! Yay!

Thanks Jane, I was trying to use the am-hm inequality because

and it looks so nice tongue. I also tried Cauchy but briefly.

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