Question

If x+y= 12 and xy=27 find the value of x^3+y^3

Answer 1

$(x + y) = 12 \\ x y = 27 \\ \\ (x + y) {}^{2} = 144 \\ x {}^{2} + y {}^{2} + 2xy = 144 \\ x {}^{2} + y {}^{2} = 144 - 54 = 90$
$x {}^{3} + y {}^{3} = (x +y)(x { }^{2} - xy + y {}^{2} ) \\ = (12)(90 - 27) = 12 \times 63$