Prove that the inequality

3a4 - 4a3b + b4 ≥ 0

holds for all real numbersaandb.

THANK YOU VERY MUCH FOR YOUR HELP!!!:)

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- Oct 12th 2007, 02:39 PMrlarachUrgent Inequality Help Please
Prove that the inequality

3a4 - 4a3b + b4 ≥ 0

holds for all real numbers**a**and**b**.

THANK YOU VERY MUCH FOR YOUR HELP!!!:) - Oct 12th 2007, 03:33 PMSoroban
Hello, rlarach!

Quote:

Prove that: . for all real numbers and

Let

I used the Factor Theorem a few times.

If , the polynomial has value 0.

. . Hence, is a factor of

Using long division: .

And we find that is a factor of the cubic.

Long division: .

. . Hence, we have: .

We see that:

. . and that: .

Therefore, for all real