已知X+Y=1,求X的三次方加Y的三次方加3XY的值
问题描述:
已知X+Y=1,求X的三次方加Y的三次方加3XY的值
答
已知x+y=1,则x^3 + y^3 +3xy
=(x+y)(x^2-xy+y^2)+3xy
=1×(x^2-xy+y^2)+3xy
=x^2-xy+y^2+3xy
= x^2+2xy+y^2
=(x+y)^2
=1^2
=1