Solve the following for x, where |x| is modulus function, [x] is the g

1.	Solve the following for x, where \|x\| is modulus function, [x] is the greatest integer function, {x} is a fractional part function.\|x2 – x – 6\| = x + 2
Answer» \|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}

Solve the following for x, where |x| is modulus function, [x] is the greatest integer function, {x} is a fractional part function.|x2 – x – 6| = x + 2

Answer»

|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}