If $p^2 = q^2$ , which of the following statements must hold true?

Correct answer marked below

p = q

p = −q

p = |q|

p = −|q|

|p| = |q|

Correct

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Explanation

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Official Explanation

Official

We start with the equation

p^2 = q^2

. To analyze this, we can take the square root of both sides:

√p^2 = √q^2

. When we take the square root of a squared variable, we obtain the absolute…

Comments

ManishMay 3, 2025

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SujoyNov 28, 2024

Great

2020MEB098Apr 17, 2024

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What this question tests

Your ability to solve absolute-value equations and inequalities by considering both cases.

Dropping the absolute value bars entirely or missing that |x| = k has two solutions when k > 0.