The solution set of x 2-6- x -8-0 isA- x - 2- x - 3B x- x- 4C- x- 3- x- 4

The correct option is B x=±2,x=±4Given x^2 6|x|+8=0 ⇒ (|x|)^2 6|x|+8 = 0 ⇒ (|x|)^2 6|x|+8 = 0 ⇒ (|x| 2)(|x| 4) = 0 ⇒ (|x| 2) = 0 or (|x| 4) = 0 ⇒ |x| = 2 ...

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Standard XI

Mathematics

Inequalities Involving Modulus Function

The solution ...

Question

The solution set of $x^{2} - 6 | x | + 8 = 0$ is .

x=±2,x=±3

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x=±2,x=±4

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x=±3,x=±4

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Solution

The correct option is B x=±2,x=±4
Given $x^{2} - 6 | x | + 8 = 0$
$\Rightarrow (| x |)^{2} - 6 | x | + 8 = 0$
$\Rightarrow (| x |)^{2} - 6 | x | + 8 = 0$
$\Rightarrow (| x | - 2) (| x | - 4) = 0$
$\Rightarrow (| x | - 2) = 0 o r (| x | - 4) = 0$
$\Rightarrow | x | = 2 o r | x | = 4$
$\Rightarrow x = \pm 2 o r x = \pm 4$

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The solution set of x2−6|x|+8=0 is .

The correct option is B x=±2,x=±4Given x2−6|x|+8=0 ⇒(|x|)2−6|x|+8=0 ⇒(|x|)2−6|x|+8=0 ⇒(|x|−2)(|x|−4)=0 ⇒(|x|−2)=0 or (|x|−4)=0 ⇒|x|=2 or |x|=4 ⇒x=±2 or x=±4

The solution set of $x^{2} - 6 | x | + 8 = 0$ is .