高校问答刘汉和王健林谁厉害:数学题两道,,要步骤
来源：百度文库 编辑：高校问答 时间：2024/05/09 04:42:38
已知m^2+m-1=0. 求m^3+2m^2-2005
已知x+y+z=4,,,x^2+y^2+z^2=2 求xy+yz+zx的值
已知x+y+z=4,,,x^2+y^2+z^2=2 求xy+yz+zx的值
1 m^2+m-1=0可得m^3+m^2-m=0
m^3+2m^2-2005=m^3+m^2-m+m^2+m-1-2004=-2004
2 x+y+z=4得(x+y+z)^2=16即x^2+y^2+z^2+2xy+2yz+2zx=16
x^2+y^2+z^2=2得xy+yz+zx=7
m^3+2m^2-2005=m*(m^2+m-1)+(m^2+m-1)-2004=-2004
(x+y+z)^2 = 4^2 = 16
(x+y+z)^2 = x^2+y^2+z^2 + 2*(xy+yz+zx) = 2+ 2*(xy+yz+zx)
xy+yz+zx = 7
1 m^3+sm^2-2005=m(m^2+m-1)+m^2+m-1-2004=2004
2 ( x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx
xy+yz+zx=(( x+y+z)^2-x^2+y^2+z^2)/2
=7
1 m^2+m-1=0可得m^3+m^2-m=0
m^3+2m^2-2005=m^3+m^2-m+m^2+m-1-2004=-2004
2 x+y+z=4得(x+y+z)^2=16即x^2+y^2+z^2+2xy+2yz+2zx=16
x^2+y^2+z^2=2得xy+yz+zx=7