Question

Find the value of.
X^{​​​​​​3}+y^{​​​​​​3}​​​​​y3-12xy+64 when x+y=-4

Answer 1

Taking cube both sides we get

(x+y)^3=-4^3= -64

now expanding x^3+ y^3+3xy(x+y)=-64

putting x+y=-4 we get

x^3+y^3+3xy(-4)= -64

or x^3+y^3-12xy+64=0

so the answer is 0.