One of the basic question from arithmetic progression chapter in which we have been asked to prove that (a−b)^2, (a^2+b^2) and (a+b)^2 are in AP.
RS Aggarwal, Class 10, chapter 5B, question no 5.
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Assume that (a−b)2,(a2+b2) and (a+b)2 are in AP.
So, difference between two consecutive terms will be same.
(a2+b2)−(a−b)2=(a+b)2−(a2+b2)
(a2+b2)−(a2+b2−2ab)=a2+b2+2ab−a2−b2
2ab=2ab
Which is true.
Hence given terms are in AP.