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 2008-04-03 01:21:57

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

inequality

Aren't they just the coolest?

Thankyou for the help

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#2 2008-04-03 01:59:07

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

Re: inequality

Hence

If you’re wondering how I went about working it out, I worked backwards from the given inequality to ab ≤ [sup]1[/sup]⁄[sub]4[/sub]. Fortunately the arrows are reversible. big_smile
­

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#3 2008-04-03 04:20:37

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

Re: inequality

Clap clap, that was great! Thankyou Jane

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#4 2008-04-07 05:31:32

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: inequality

that was cool jane, but you can also do it really easy with jensen's inequality:
the function

is strictly convex for x>0. thus we have

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