How many positive real number x satisfy the equation $x^{3} - 3 | x | + 2 = 0$ ?

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Solution

The correct option is A 1
$x^{3} - 3 | x | + 2 = 0$ [let x > 0]
$x^{3} - 3 x + 2 = 0$
$(x - 1) (x^{2} + x - 2) = 0$
$x = 1, x = \frac{- 1 + \sqrt{9}}{2} = 1$
Now, let x < 0
$x^{3} + 3 x + 2 = 0$
no solution
$x = 1$ only one solution

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