What is the number of real solutions for the | vedclass

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Question

(A) Given the equation $x^2 - 3|x| + 2 = 0$.Since $x^2 = |x|^2$,we can rewrite the equation as $|x|^2 - 3|x| + 2 = 0$.Let $t = |x|$,where $t \geq 0$.

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Given the equation $x^2 - 3|x| + 2 = 0$.Since $x^2 = |x|^2$,we can rewrite the equation as $|x|^2 - 3|x| + 2 = 0$.Let $t = |x|$,where $t \geq 0$. The equation becomes $t^2 - 3t + 2 = 0$.Factoring the quadratic equation: $(t - 1)(t - 2) = 0$.This gives $t = 1$ or $t = 2$.Case $1$: $|x| = 1$ implies $x = 1$ or $x = -1$.Case $2$: $|x| = 2$ implies $x = 2$ or $x = -2$.Thus,the real solutions are $x \in \{-2, -1, 1, 2\}$.The total number of real solutions is $4$.

What is the number of real solutions for the equation $x^2 - 3|x| + 2 = 0$?

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