If x = a(b - c), y = b(c – a) and z = c(a - b) , find the value of (x/a)3 + (y/b)3 + (z/c)3?
We know the identity a³ + b³ + c³ - 3abc = (a+b+c) (a2 + b2 + c2 – ab – bc - ca) x = a(b - c), y = b(c - a), z = c(a - b) x/a = b - c, y/b = c - a, z/c = a - b x/a + y/b + z/c = b - c + c - a + a - b = 0 According to the identity If a + b + c = 0 Then, a³ + b³ + c³ = 3abc (x/a)3 + (y/b)3 + (z/c)3 = (3xyz)/(abc)
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