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 ge 0 " 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`
`implies 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)le0`
or `-1 le x le 2`


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