Given that p is a negative number and $0 < s < |p|$ , which of the following must also be a negative number?

Correct answer marked below

(p+s)^2

(p-s)^2

(s-p)^2

p^2-s^2

s^2-p^2

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Explanation

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Official Explanation

Official

Let's choose specific values for our variables to analyze the options. Let p = -3 and s = 2, which satisfies the condition

0 < s < |p|

. Now we evaluate each option:

(A) becomes (-1)^2 = 1, which is not negative.

(B) results in (-5)^2 = 25, also not negative.…

Comments

HuanJun 18, 2024

finally understood this

NMay 30, 2024

Can someone explain it other way?

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.