Question

If x + y = 12 and xy = 27, find the value of x³ + y3

Answer 1

Answer:

$given \: that : \\ x + y = 12 \: \: \: \: \: \: xy = 27 \\ (x + y) {}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) \\ {(12)}^{3} ={ x}^{3} + {y}^{3} + 3(27)(12) \\ 1728 = {x}^{3} + {y}^{3} + 972 \\ {x}^{3} + {y}^{3} = 1728 - 972 = 756$

Answer 2

X^3+y^3= (x+y)( x^2-xy+y^2)
= (x+y) {( x+y)^2-3xy}
= 12{144-3x27}
= 12(63) = 796