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)`
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(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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