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Question
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
x2 + 7 |x| + 12 = 0
Solution
x2 + 7 |x| + 12 = 0 ...(1)
Case 1:
Let x ≥ 0
∴ |x| = x
∴ equation (1) becomes x2 + 7x + 12 = 0
∴ (x + 4)(x + 3) = 0
∴ x = – 4 or x = – 3
But x ≥ 0
∴ for x ≥ 0, there is no solution
Case 2:
Let x < 0
∴ |x| = – x
∴ equation (1) becomes x2 – 7x + 12 = 0
∴ (x – 3)(x – 4) = 0
∴ x = 3 or x = 4
But x < 0
∴ for x < 0, there is no solution
∴ the equation has no solution
∴ solution set is { }.
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