Look for the Negative One

Algebra Level 2

If b b is a negative number such that 0 < a < ∣ b ∣ 0 < a < |b| , where a a is an integer, then which of the following must also be negative?

A. ( a + b ) 2 (a+b)^2

B. ( a − b ) 2 (a-b)^2

C. ( b − a ) 2 (b - a)^2

D. b 2 − a 2 b^2- a^2

E. a 2 − b 2 a^2-b^2

A B C E D

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Stephen Mellor
Feb 13, 2018

A,B and C are all perfect squares so ≥ 0 \geq 0 . ∣ b ∣ > ∣ a ∣ ⇒ b 2 > a 2 |b| > |a| \Rightarrow b^2 > a^2 . Therefore, b 2 − a 2 > 0 b^2 - a^2 > 0 and a 2 − b 2 < 0 a^2 - b^2 < 0 , so the answer is E \boxed{\text{E}}

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Thank you for sharing your solution.

Hana Wehbi - 3 years, 3 months ago

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