Question

if a,b ,c arein AP, find the value of a3-8b3+c3+6abc

Answer 1

Answer:

HOPE THIS HELPS YOU : )

If a,b, and c are in A.P.

∴ a+c=2b -------(i)

First of all we need to prove that : a^3 - 8b^3 + c^3 = -6abc

a^3+c^3-8b^3=-6abc

a^3+(-2b)^3+c^3=3a(-2b)c

Thus the form is :

x^3+y^3+z^3=babc

For this we know : x+y+z=0

a+(-2b)+c=0

a+c=2b

We have already proved it

So, Our asumption is correct

a^3-8b^3+c^3=-6abc

So, a^3-8b^3+c^3+6abc=0