The sum of the solutions of the equation - x 2-10 x -21- x -3- isA- 17B- 18C- 14D- 21

The correct option is A 17| x^2 10x+21|=| x 3| ⇒| x^2 10x+21| | x 3|=0 nbsp; ⇒ |x 3||x 7| | x 3|=0 nbsp; ⇒ |x 3| (|x 7| 1 )=0 ⇒ nbsp;|x 3|=0 or |x 7 |=1 ...

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Standard XII

Mathematics

Absolute Value Function

The sum of th...

Question

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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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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The sum of the solutions of the equation |x2−10x+21|=|x−3| is

The correct option is A 17|x2−10x+21|=|x−3| ⇒|x2−10x+21|−|x−3|=0 ⇒|x−3||x−7|−|x−3|=0 ⇒|x−3|(|x−7|−1)=0 ⇒|x−3|=0 or |x−7|=1 ⇒x=3 or, x−7=±1⇒x=6,8 Sum of the solutions of the equation is 3+6+8=17

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