Number of positive integral solution of the $| x | | x - 5 | + | 24 - 3 x | = | x^{2} - 8 x + 24 |$ is

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Solution

$| x^{2} - 5 x | + | 24 - 3 x | = | x^{2} - 8 x + 24 | | a | + | b | = | a + b | \Rightarrow a b \geq 0 ∴ (x^{2} - 5 x) (24 - 3 x) \geq 0 x (x - 5) (x - 8) \leq 0 x \in (- \infty, 0] \cup [5, 8]$

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