Question

The roots of |x-2{{|}^{2}}+|x-2|-6=0
are [UPSEAT 2003]
A) 0, 4 B) -1, 3 C) 4, 2 D) 5, 1

Answer 1

Hi ,

| x - 2 |² + | x - 2 | - 6 = 0

| x - 2 |² + 3| x - 2 | - 2| x - 2 | - 6 = 0

| x - 2 | ( | x - 2 | + 3 ) - 2 ( | x - 2 | + 3 ) = 0

( | x - 2 | + 3 ) ( | x - 2 | - 2 ) = 0

Therefore ,

( | x - 2 | + 3 ) = 0 or ( | x - 2 | - 2 ) = 0

| x - 2 | = - 3 or | x - 2 | = 2

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

x - 2 = 3 or x = 2 + 2

x = 3 + 2 or x = 4

x = 5 or x = 4

I hope this helps you.

: )