Q. 84.9( 7 Votes )

Show that (a–b)2, (a2+b2) and (a + b)2 are in A.P.

Answer :

The terms given below are : (a–b)2, (a2+b2) and (a + b)2

Common difference, d1 = a2 + b2 – (a – b)2

d= a2 + b2 – (a2 + b2 - 2ab)

d= a2 + b2 – a2 - b2 + 2ab

d1= 2ab

Common difference, d2 = (a + b)2 – (a2 + b2)

d2 = a2 + b2 + 2ab – a2 –b2

d2 = 2ab

Since, d1 = di.e. the common difference is same. 

Therefore, the given terms are in A.P.

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