Question

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Answer 1

Answer:

Given (a ^ 2 - b ^ 2) ^ 3 + (b ^ 2 - c ^ 2) ^ 3 + (c ^ 2 - a ^ 2) ^ 3 = 3(a + b) * (b + c) (c+a)(a-b)(b-c)(c-a) Consider LHS:(a²-b²)³+(b²-c²)³+(c²-a²)³ We know that if x + y + z = 0 then x3 + y3 + 23 = 3xyz Here x = a ^ 2 - b ^ 2, y = b ^ 2 - c ^ 2 and z = c ^ 2 - a ^ 2; a ^ 2 - b ^ 2 + b ^ 2 - c ^ 2 + c ^ 2 - a ^ 2 = 0 Hence (a ^ 2 - b ^ 2) ^ 3 + (b ^ 2 - c ^ 2) ^ 3 + (c ^ 2 - a ^ 2) ^ 3 = 3(a ^ 2 - b ^ 2) (b²-c²)(c²-a²)³ = 3(a + b)(a - b)(b + c)(b − c)(c + a)(c − a) = = 3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a)

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