Question

24) Solve: (a + b + 2c)3 + (b + c – 2a)3 + (a + a - 2b)3
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Answer 1

Answer:

Let x = a + b + 2c

y = b + c - 2a

z = c + a - 2b

now, x + y + z = 0

This implies, x^3 + y^3 + z^3 = 3xyz

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

Hence the required solution