The number of solution of the equation ` |x-x^(2)-1| = |2x -3-x^(2)|` is
(1) 0 (2) 1 (3) (4) Infinitely many

Explanation

we have
`|x-x^(2)-1| = |2x-3-x^(2)|`
` Rightarrow |x^(2)-x+1| = |x^(2)-2x+3|`
`Rightarrow | (x -1/2)^(2) +3/4| =|(x-1)^2 +2|`
` Rightarrow x^(2) -x +1 =x^(2)-2x +3 , " as " |x| =x " when " x gt 0`
` Rightarrow 2x- x= 3 -1 `
` Rightarrow x=2 `
The given equation has only one root i.e, 2.