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

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**Thanh Vân****Member**- Registered: 2011-07-17
- Posts: 10

Let a,b,c,d be positive real numbes. prove that

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi Thanh Vân,

Welcome to the forum!

*Last edited by gAr (2011-07-17 04:19:09)*

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

**Thanh Vân****Member**- Registered: 2011-07-17
- Posts: 10

Oh. Hi gAr. I don't understand your proof.

Why you have

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

I thought since 8 is the minimum value LHS can have, we may write like that.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,964

Hi;

For anyone else wishing to work on the problem here it is latexed.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

**Thanh Vân****Member**- Registered: 2011-07-17
- Posts: 10

I thinks idea of gAr is wrong and can't use it to prove inequality. It can solve by Cauchy Schwarz Inequality and AM-GM Inequality very beautiful.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi Thanh Vân,

Yes, I was wrong. I made wrong assumption without checking.

Anyway, I could prove

and

But unable to get anywhere.

*Last edited by gAr (2011-07-21 17:02:17)*

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

Pages: **1**