Find the values of $x$ satisfying the equation
$∣ ∣ x^{2} - 9 ∣ ∣ + ∣ ∣ x^{2} - 1 ∣ ∣ + ∣ ∣ x^{2} - 5 x + 6 ∣ ∣ = 0$

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Solution

R.E.F image
$| (x + 3) (x - 3) | + | (x + 1) (x - 1) | + | (x - 2) (x - 3) | = 0$
$f (x) = 3 x^{2} - 5 x - 4$ $x ϵ (- \infty, - 3)$
$x^{2} - 5 x + 14$ $x ϵ (- 3, - 1)$
$- x^{2} - 5 x + 16$ $x ϵ (- 1, 1)$
$x^{2} - 5 x + 14$ $x ϵ (1, 2)$
$- x^{2} + 5 x + 2$ $x ϵ (2, 3)$
$3 x^{2} - 5 x - 4$ $x ϵ (3, \infty)$

$| (x + 3) (x - 3) | > 0$
$x ϵ (- \infty, - 3) \cup (3, \infty)$
$| (x + 1) (x - 1) > 0$
$x ϵ (- \infty - 1) \cup (1, \infty)$
$| (x - 2) (x - 3) > 0$
$x ϵ (- \infty, 2) \cup (3, \infty)$

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