2011/053) find the relation between a and b when a^3+b^3 = 8 - 6 ab

take 8 to the left

a^3+b^3-8 = -6 ab
or a^3+b^3 + (-2)^3 = 3(-2) a b

as x^3 +y^3 + z^3 = 3xyz then x = y = z or x + y+ z = 0

comparing we get a = b = -2 or a + b- 2 = 0

that is a= b = -2 or a + b = 2