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Question
Answer the following:
Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function
|x2 − x − 6| = x + 2
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Solution
|x2 − x − 6| = x + 2 ...(i)
R.H.S. must be non-negative
∴ x ≥ − 2 ...(ii)
|(x – 3) (x + 2)| = x + 2
∴ (x + 2) |x – 3| = x + 2 as x + 2 ≥ 0
∴ |x – 3| = 1 if x ≠ – 2
∴ x – 3 = ± 1
∴ x = 4 or 2
∴ x = – 2 also satisfies the equation
Solution set = {–2, 2, 4}
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