A binary operation is defined by x y =\(x^y\). If x 2 = 12 - x, find the possible values of x
The correct answer is B. 3,-4
Since the binary operation is defined by x y = \(x^y\), we can rewrite the given equation x 2 = 12 - x as:
\(x^2 = 12 - x\).
Rearranging this equation, we get \(x^2 + x - 12 = 0\).
This is a quadratic equation, which we can solve using the quadratic formula:
\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\),
a = 1, b = 1, and c = -12.
Substituting these values into the formula, we get:
\(x = \frac{-1 \pm \sqrt{1 + 48}}{2} = \frac{-1 \pm 7}{2}\).
This gives us two possible values for x: \(x = \frac{-1 + 7}{2} = 3\) and \(x = \frac{-1 - 7}{2} = -4\). Therefore, the possible values of x are 3 and -4.
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