In A B C , if A, B and C are in A P , then a^2 b^2 and c^2 are in

Step-by-step solution

It is given, A, B and C are in AP . array ll & 2 B= A+ C & 2 B B = A A + C C & A a = B b = C c =k & 2 B k b = A a k + C c k & 2 B b = A a + C c array aligned & 2 b [ a^2+c^2-b^2 2 a c ]= 1 a [ b^2+c^2-a^2 2 b c ] &+ 1 c [ a^2+b^2-c^2 2 a b ] aligned aligned & 2 (a^2+c^2-b^2 ) 2 a b c = 1 2 a b c & [ (b^2+c^2-a^2 )+ (a^2+b^2-c^2 ) ] aligned array rlrl & & 2 (a^2+c^2-b^2 ) & =2 b^2 & a^2+c^2 & =2 b^2 array a^2, b^2 and c^2 are in AP.