x + y = 6.......................(1)
x^3 + y^3 =60.............(2)
y =6 - x
Solve for x:
(6 - x)^3 + x^3 = 60
Expand out terms of the left hand side:
18 x^2 - 108 x + 216 = 60
Divide both sides by 18:
x^2 - 6 x + 12 = 10/3
Subtract 12 from both sides:
x^2 - 6 x = -26/3
Add 9 to both sides:
x^2 - 6 x + 9 = 1/3
Write the left hand side as a square:
(x - 3)^2 = 1/3
Take the square root of both sides:
x - 3 = 1/sqrt(3) or x - 3 = -1/sqrt(3)
Add 3 to both sides:
x = 3 + 1/sqrt(3) or x - 3 = -1/sqrt(3)
Add 3 to both sides
x = 3 + 1/sqrt(3) and y = 3 - 1/sqrt(3) OR y = 3 + 1/sqrt(3) and x = 3 - 1/sqrt(3)