Help!! Math problem #4?

Question

4. Prove that the inequality 3(a)^2 – 4((a)^3)*b + b^4 = 0 holds for all real numbers a and b.

Sorry, the inequality should look like this:
3a^4 – 4(a^3)*b + b^4 is greater than or equal to 0

Answer 1

First off, this is not an inequality; it's an equality (notice the "equals" sign).

And it doesn't hold for all real numbers a and b.

Here is a counterexample:
Let a = 0 and b = 1
3(a)^2 – 4((a)^3)*b + b^4
= 0 - 0 + 1
= 1
1 is not equal to 0 so I have proven the equality doesn't not hold for all real numbers a and b.

Answer 2

First: what you wrote was an equality, not an inequality.

Second: even if it were an inequality, it would be false:

for a = 0, b = 1, the left hand side is just b^4 which is 1.

for a = 2, b = 1 the left hand side is:
3(2)^2 - 4(2)^3 + b^4 = 3x4 - 4x8 + 1 = 12 - 32 + 1 = -19