1.

Solve the following (i) | x-2 | = (x-2) (ii) |x+3 |=-x-3 (iii) `|x^2-x|=x^2-x ` (iv) `|x^2-x-2|=2 +x-x^2`

Answer» (i) `|x-2|= (x-2), if x-2 le 0 of or x ge 2 `
(ii) `| x+3 | =-x-3, if x+3 le 0 or x le -3`
(iii) `|x^2-x|=x^2-x, if x^2- x ge 0 `
or `x(x-1) ge 0 `
`rArr x in (-oo ,0] cup [1, oo)`
(iv) `|x^2 - x -2 |=2 + x - x^2`
or `x^2-x -2 le 0 `
or `(x-2)(x+1) le 0 `
`or -1 le x le 2 `


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