If a@b = a^4 - b^3/a - b, then for how many real values of a does a@1 = 0?

Answer 1

To find for how many real values of a the equation a @ 1 = 0, we need to substitute a = 1 into the expression for a @ b and solve for b:

a @ b = a^4 - b^3 / (a - b)

Setting a = 1, we have:

1 @ b = 1 - b^3 / (1 - b)

To make this equation equal to 0, the numerator must be equal to 0:

1 - b^3 = 0

This equation has one real solution: b = 1.

Therefore, there is only one real value of a for which a @ 1 = 0.