alleryIs (a + b)² > a² + b² always true for non-zero a, b?
AYes, always
BNo — only when 2ab > 0 (i.e. a and b have the same sign)
CNever
DOnly when a = b
Answer & Solution
Correct answer: B. No — only when 2ab > 0 (i.e. a and b have the same sign)
(a + b)² = a² + 2ab + b².
So (a + b)² − (a² + b²) = 2ab.
This is positive iff 2ab > 0, i.e. when a and b are both positive or both negative.
If they have opposite signs (ab < 0), (a+b)² < a² + b².
When ab = 0, they are equal.
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