Is (a + b)² a² + b² always true for non-zero a, b?

Question

Is (a + b)² > a² + b² always true for non-zero a, b?

Accepted 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.

Answer

Yes, always

Answer

Never

Answer

Only when a = b

Is (a + b)² > a² + b² always true for non-zero a, b?

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