若m和n互为相反数,且m.n均不为0,x和y互为倒数,求xy(m³+n³)-m÷n+x²y²
问题描述：
若m和n互为相反数,且m.n均不为0,x和y互为倒数,求xy(m³+n³)-m÷n+x²y²
答
若m和n互为相反数,且m.n均不为0,x和y互为倒数,
则m+n=0,m÷n=-1,xy=1
xy(m³+n³)-m÷n+x²y²
=xy(m+n)(m²-mn+n²)-m÷n+1
=1-m÷n
=1-(-1)
=2
答
m和n互为相反数,m=-n
m³+n³=(m+n)(m²-mn+n²)=0
m,n≠0,m/n=-1
xy互为倒数,x=1/y xy=1
xy(m³+n³)-m÷n +x²y²
=0-(-1)+(xy)²
=1+1
=2