Find the number of solution of $x^{2} + | x - 1 | = 1$ .

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Solution

$x^{2} + | x - 1 | = 1$
If $x - 1 \geq 0 \Rightarrow x \geq 1$
$x^{2} + x - 1 = 1$
$x^{2} + x - 2 = 0$
$(x + 2) (x - 1) = 0$
$x = - 2, 1$
$x = - 2$ , Not possible,
So, $x = 1$ is a solution.
If $x - 1 < 0 \Rightarrow x < 1$
$x^{2} + 1 - x = 1$
$x^{2} - x = 0$
$x = 0, 1$
$x = 0$ is also a solution
$x = 0, 1$ solutions.
$2$ solutions.

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