If are in AP, prove that a 2 (b + c), b 2 (c + a), c 2 (a + b) are in AP.

Question

Philoid · Accepted Answer

To prove: a²(b + c), b²(c + a), c²(a + b) are in A.P.

Given: are in A.P.

Proof:are in A.P.

are in A.P.

If each term of an A.P. is multiplied by a constant, then the resulting sequence is also an A.P.

Multiplying the A.P. with (abc)

, are in A.P.

are in A.P.

⇒ [(a²c + a²b)], [ab² + b²c], [c²b + ac²] are in A.P.

On rearranging,

⇒ [a²(b + c)], [b²(c + a)] , [c²(a + b)] are in A.P.

Hence Proved