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Shiw that (a-b)2,(a2+b2)and (a+b)2 are in …

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Shiw that (a-b)2,(a2+b2)and (a+b)2 are in AP

Posted by Amit Kumar Thakur 6 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

{tex}(a^2+b^2)-(a-b)^2=a^2+b^2-(a^2+b^2-2ab)=a^2+b^2-a^2-b^2+2ab=2ab{/tex}
{tex}(a+b)^2-(a^2+b^2)=(a^2+b^2+2ab)-a^2-b^2=a^2+b^2+2ab-a^2-b^2=2ab{/tex}
Since (a²+b²)-(a-b)²=(a+b)²-(a²+b²),
(a-b)², (a²+b²) and (a+b)² are in AP.

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