a maths question

|x - 2|(x - 3) = 2

(x - 2)(x - 3) = 2 or –(x - 2)(x - 3) = 2

x2 – 5x + 6 = 2 or –x2 + 5x – 6 = 2

x2 – 5x + 4 = 0 or x2 – 5x + 8 = 0

x = {-(-5) ± √[(-5)2 – 4(1)(4)]} / 2 or x = {-(-5) ± √[(-5)2 – 4(1)(8)]} / 2

x = (5 ± √9) / 2 or x = (5 ± √-7) / 2 (rejected)

x = (5 + 3) / 2 or (5 - 3) / 2

x = 4 or 1

2007-12-02 09:54:07 補充：
x = 1 should be rejected.Verify:Put x = 1 into the equation│1 - 2│(1 - 3)= 1(-2)= -2 ≠ 2So, 1 is not the correct answer.

When x<2
∴ -(x-2)(x-3)=2
(x-2)(x-3)=-2
x^2-5x+8=0
∴no solution

When x≧2
∴(x-2)(x-3)=2
x^2-5x+6-2=0
x^2-5x+4=0
x=4 or 1

put x=1 into equation
L.H.F=∣1-2∣(1-3)=-2
∴x=1 (rejected)
put x=4 into equation
L.H.F=∣4-2∣(4-3)=2
∴x=4 is correct

for all
x=4

| x-2 |(x-3)=2

Case (1), x < 2,
|x - 2| = 2 - x
So,
| x-2 |(x-3) = 2
(2 - x)(x - 3) = 2
-x^2 + 5x - 6 = 2
x^2 - 5x + 8 = 0
So, no solution as △ < 0

Case (2), x ≧ 2,
|x - 2| = x - 2
So,
| x-2 |(x-3) = 2
(x - 2)(x - 3) = 2
x^2 - 5x + 6 = 2
x^2 - 5x + 4 = 0
(x - 4)(x - 1) = 0
x = 4 or 1 (rejected)

So overall solution: x = 4

| x-2 |(x-3)=2