Q. 19

If a2, b2, c2are in A.P. then show that are also in A.P.

Answer :

Given, a2, b2 and c2 are in A.P.


We know that when t1, t2, t3 … are in A.P., t3 – t2 = t2 – t1


b2 – a2 = c2 – b2


We know that a2 – b2 = (a – b) (a + b)


(b – a) (b + a) = (c – b) (c + b)


=


Dividing by (c + a) on both sides,


=


=



Hence, , and are in A.P.


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