A binary operation * is defined by x * y = x

^{y}. If x * 2 = 12 – x, find the possible values of x-
**A.**

3,4 -
**B.**

3,-4 -
**C.**

-3,4 -
**D.**

-3,-4

##### Correct Answer: Option B

##### Explanation

x * y = x^{y}

x * 2 = 12 – x

Thus by comparison,

x = x, y = 2

But x * y = x * 2

x^{y} = 12 – x

x^{2} = 12 – x

x^{2} + x – 12 = 0

x^{2} + 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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