1.若x+y+z=6,x³+y³+z³=36,xyz=6,则yz+zx+xy=

1。(x+y+z)^3=(x^2+y^2+z^2+2xy+2yz+2zx)(x+y+z)=x^3+y^3+z^3+3x^2y+3x^2z+3xy^2+3y^2z+3xz^2+3yz^2+6xyz=36+36+3(x^2y+x^2z+y^2x+y^2z+z^2x+z^2y)=216x^2y+x^2z+y^2x+y^2z+z^2x+z^2y=48x^2(6-x)+y^2(6-y)+z^2(6-z)=486(x^2+y^2+z^2)-(x^3+y^3+z^3)=48x^2+y^2+z^2=14(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)=14+2(xy+yz+zx)=36xy+yz+zx=112。a(a-1)-(a^2-b)=-20a^2-a-a^2+b=-20a-b=20(a^2+b^2)/2-ab=[(a-b)^2+2ab]/2-ab=(a-b)^2/2+ab-ab=20^2/2=2003。a^3+3ab-b^3=(a^3-b^3)+3ab=(a-b)(a^2+ab+b^2)+3ab=-a^2-ab-b^2+3ab=-a^2+2ab-b^2=-(a-b)^2=-(-1)^2=-14。一般的,对于正整数m,n 且m>nn/m-(n+1)/(m+1)=[(n+1)m-n(m+1)]/[m(m+1)]=(mn+m-mn-n)/[m(m+1)]=(m-n)/[m(m+1)]>0对于本题：A>B5。a+b+c=0c=-(a+b)a^3+b^3+c^3=0(a+b)(a^2-ab+b^2)+c^3=0-c(a^2-ab+b^2)+c^3=0c(a^2-ab+b^2-c^2)=0c[(a+b)^2-3ab-c^2]=0c(c^2-3ab-c^2)=03abc=0a,b,c中至少有一为0,又a+b+c=0,另两数互为相反数,设为t和-ta^5+b^5+c^5=0+t^5+(-t)^5=0a^5+b^5+c^5=06。a+1/a=5a^2+1/a^2=a^2+2+1/a^2-2=(a+1/a)^2-2=25-2=237。x^2+y^2=(x+y)^2-2xy=(-10)^2-2×16=100-32=68(x+2)(y+2)=xy+2(x+y)+4=16+2(-10)+4=0