I have to Prove (a+b)^2 + (b+c)^2 + (c+a)^2 >= 4(ab + bc + ac)

I multiplied out both sides and then move everything to the left, but I don't know what I should do after that.

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- July 5th 2006, 05:04 PMNichelle14Another proof
I have to Prove (a+b)^2 + (b+c)^2 + (c+a)^2 >= 4(ab + bc + ac)

I multiplied out both sides and then move everything to the left, but I don't know what I should do after that. - July 5th 2006, 07:32 PMmalaygoelQuote:

Originally Posted by**Nichelle14**

Keep Smiling

Malay - July 5th 2006, 07:54 PMThePerfectHackerQuote:

Originally Posted by**Nichelle14**

----

If you play your cards right this is the "Cauchy-Swarchtz Inequality".

Let,

Then,

Now,

And,

Thus,

- July 6th 2006, 10:18 AMSoroban
Hello, Nichelle14!

Quote:

Prove that: .

I multiplied out both sides and then move everything to the left. . . . Not recommended

Multiply out the left side and we have:

. .**LHS**

Since are real numbers: .

Multiply by

Add to both sides:

. .

. . . . . . . . This is LHS

Therefore: .