The number of solutions for the equation x^2 | vedclass

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Question

(A) Given equation is $x^2 - 5|x| + 6 = 0$.Since $|x|^2 = x^2$,we can write the equation as $|x|^2 - 5|x| + 6 = 0$.Let $|x| = t$,where $t \ge 0$. Then

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Given equation is $x^2 - 5|x| + 6 = 0$.Since $|x|^2 = x^2$,we can write the equation as $|x|^2 - 5|x| + 6 = 0$.Let $|x| = t$,where $t \ge 0$. Then the equation becomes $t^2 - 5t + 6 = 0$.Factoring the quadratic: $(t - 2)(t - 3) = 0$.This gives $t = 2$ or $t = 3$.Case $1$: $|x| = 2 \implies x = 2, -2$.Case $2$: $|x| = 3 \implies x = 3, -3$.Thus,the solutions are $x \in \{2, -2, 3, -3\}$.There are $4$ solutions in total.

The number of solutions for the equation $x^2 - 5|x| + 6 = 0$ is

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