(2a-b)^3+(b-c)^3+8(c-a)^3
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Gaurav Seth 4 years, 2 months ago
The given equation is,
(2a - b)³ + (b - 2c)³ + 8(c - a)³
= (2a - b)³ + (b - 2c)³ + (2c - 2a)³
Let x = (2a - b) ; y = (b - 2c) ; z = (2c - 2a)
Now,
x + y+ z = (2a - b) + (b - 2c) + (2c - 2a) = 0
Since, x + y + z = 0, then,
x³ + y³ + z³ = 3xyz
⇒ (2a - b)³ + (b - 2c)³ + (2c - 2a)³ = 3(2a - b) (b - 2c) (2c - 2a)
⇒ (2a - b)³ + (b - 2c)³ + 8(c - a)³ = 6(2a - b) (b - 2c) (c - a)
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