A binary operation * is defined by x * y = xy. 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 = xy
x * 2 = 12 – x
Thus by comparison,
x = x, y = 2
But x * y = x * 2
xy = 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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