A binary operation * is defined by x * y = x^y. If x * 2 = 12 - x, find the possible values of x

3,4

3,-4

-3,4

-3,-4

Correct answer is B

x * y = x^y
x * 2 = 12 - x

Thus by comparison,

x = x, y = 2

But x * y = x * 2

x^y = 12 - x

x² = 12 - x

x² + x - 12 = 0

x² + 4x - 3x - 12 = 0

x(x + 4) - 3(x + 4) = 0

(x - 3)(x + 4) = 0

x - 3 = 0 or x + 4 = 0

So x = 3 or x = -4

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A binary operation * is defined by x * y = x^y. If x * 2 = 12 - x, find the possible values of x