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Rajan@2021
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Show that (a−b)^2, (a^2+b^2) and (a+b)^2 are in AP.

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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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  1. Assume that (ab)2,(a2+b2) and (a+b)2 are in AP.
    So, difference between two consecutive terms will be same.
    (a2+b2)(ab)2=(a+b)2(a2+b2)
    (a2+b2)(a2+b22ab)=a2+b2+2aba2b2
    2ab=2ab
    Which is true.
    Hence given terms are in AP.

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