Prove that the inequality
3a4 - 4a3b + b4 ≥ 0
holds for all real numbers a and b.
THANK YOU VERY MUCH FOR YOUR HELP!!!
Hello, rlarach!
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