Question

If a b c are in ap then prove that (a-c)2=4(b2-ac)

Answer 1

Answer:

b-a=c-b

b+b=a+c

2b=a+c

a=2b-c ......(1)

put in LHS of given proof

(2b-c-c)^2= (2b-2c)^2

=4(b-c)^2

=4(b^2+c^2-2bc)

=4{b^2 +c(c-2b)}

=4(b^2-ac) using (1)