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Inequalities Involving Modulus Function

The set of ex...

Question

The set of exhaustive values of $x$ which satisfying the equation $| x^{2} - 5 x + 4 | + | x^{2} - 7 x + 10 | = 2 | x - 3 |$ is given by

R

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[1, 2] \cup [4, 5]

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(- \infty, 1] \cup [2, 4] \cup [5, \infty]

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{1, 2, 4, 5}

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Solution

The correct option is B $[1, 2] \cup [4, 5]$
If $| a | + | b | = | a - b |,$ then $a b \leq 0$
$\Rightarrow (x^{2} - 5 x + 4) (x^{2} - 7 x + 10) \leq 0$
$\Rightarrow (x - 1) (x - 4) (x - 2) (x - 5) \leq 0$

$∴ x \in [1, 2] \cup [4, 5]$

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