Question

X + Y equal to 12 and xy equal to 32 find the value of x cube + Y cube

Answer 1

$x + y = 12 \: \: \: \: \: \: - - - (1)\\ xy = 32 \: \: - - - - - (2) \\ \\ from \: eq \: (1) \\ x = 12 - y \: \: \: \: \: - - - - (3) \\ putting \: eq \: (3) \: in \: \: (2)\\ (12 - y)(y) = 32 \\ {y}^{2} + 12y - 32 = 0 \\ {y}^{2} + 8y + 4y - 32 \\ y(y + 8) - 4(y + 8) = 0 \\ (y - 4) = 0 \: \:( y + 8) = 0 \\ y = 4 \: \: y = - 8 \\ \\ x + 4 = 12 \\ x = 8 \\ {x}^{3} + {y}^{3} \\ = {8 }^{3} + {4}^{3} \\ = 512 + 64 \\ = 576$