已知x-y=xy=3.求(x+y)的平方及x的三次方-y的三次方_数学解答

已知x-y=xy=3.求(x+y)的平方及x的三次方-y的三次方

人气：468 ℃　时间：2019-10-31 13:30:01

解答

(x+y)^2
=(x-y)^2+4xy
=3^2+4*3
=9+12
=21
x^3-y^3
=(x-y)(x^2+xy+y^2)
=(x-y)(x^2-2xy+y^2+3xy)
=(x-y)[(x-y)^2+3xy]
=3*[3^2+3*3]
=3*18
=54