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A binary operation * is defined by x * y = xy. If x *...

Mathematics
JAMB 2014

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
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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

There is an explanation video available below.


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Explanation Video

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