Question

Ifa+3b+2c=0,Prove that a3 +27b3 +8c3 =18abc

Answer 1

Answer:

18

Step-by-step explanation:

Given, a+3b+2c = 0

3b = -(2c+a) ———(1)

a^3 + 27b^3 + 8c^3

=a^3 + (3b)^3 + 8c^3

Put (1),

=a^3 + {-(2c+a)}^3 + 8c^3

= a^3 - (8c^3 + a^3 + 12ac^2 + 6a^2c) + 8c^3

= a^3 - 8c^3 - a^3 - 12ac^2 - 6a^ 2c + 8c^3

= -12ac^2 - 6a^2c

= -6ac (2c+a)

Put (1),

= 6ac * 3b

= 18abc (ans)