Question

Without actually calculating the cubes,find the value of each of the following: (12)3+(7)3+(5)3

Answer 1

a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

let (a + b + c)=0

anything * zero = zero

so

a3 + b3 + c3 - 3abc = 0 (a2 + b2 + c2 - ab - bc - ca)

a3 + b3 + c3 - 3abc = 0

a3 + b3 + c3 = +3abc

so 12^3 + 7^3 + 5^3 = 3 * (12 * 7 * 5)