Given that |a| = |b| and ab = 0, which of the following statements must hold true?

Answer Choices

Correct answer marked below

ab^2>0

a^2b>0

a+b=0

Correct

\frac{a}{(b+2)}=3

\frac{1}{a}+\frac{1}{b}=\frac{1}{3}

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Explanation

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Official Explanation

Official

We know that |a| = |b| and ab = 0. This means either a = 0 and b ≠ 0, or b = 0 and a ≠ 0, or both a = b = 0. For simplicity, let's consider the case where a = b = 0, which satisfies |a| = |b|. Now, we will substitute a = 0 and b = 0 into the options A-D to see which one remains true. A.

ab^2>0

is false since 0 > 0 is not true. Eliminate A. B.

a^2b>0

is…

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Comments

ChrisMar 13, 2024

Love how you solved this

YashikaMay 3, 2025

greatt question!

What this question tests

What it tests

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

Common trap

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