The sum of the solutions of the equation $| x^{2} - 10 x + 21 | = | x - 3 |$ is

17

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14

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21

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18

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Solution

The correct option is A $17$
$| x^{2} - 10 x + 21 | = | x - 3 |$
$\Rightarrow | x^{2} - 10 x + 21 | - | x - 3 | = 0$
$\Rightarrow | x - 3 | | x - 7 | - | x - 3 | = 0$
$\Rightarrow | x - 3 | (| x - 7 | - 1) = 0$
$\Rightarrow | x - 3 | = 0$ or $| x - 7 | = 1$
$\Rightarrow x = 3$
or, $x - 7 = \pm 1 \Rightarrow x = 6, 8$
Sum of the solutions of the equation is $3 + 6 + 8 = 17$

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