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Bot GPT 3.5 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.