已知x+y+z=1,x²+y²+z²=2求xy+yz+xz的值
已知x+y+z=1,x²+y²+z²=2求xy+yz+xz的值
(x+y+z)²=1 , x²+2xy+y²+2(x+y)z+z²=1, x²+y²+z²+2(x+y)z+2xy=1
xy+yz+xz=-1/2
已知x+y+z=a,xy+yz+xz=b,求x²+y²+z²
(x+y+z)^2=a^2
x^2+y^2+z^2+2xy+2yz+2xz=a^2
x^2+y^2+z^2+2b=a^2
x^2+y^2+z^2=a^2-2b
已知x²+y²+z²=8,xy+yz+xz=4,则(x+y+z)²的值是
(x+y+z)²=x²+y²+z²+2（xy+yz+xz）=16
已知x+y+z=10，xy+xz+yz=8，求x²+y²+z²的值
(x+y+z)²=10²
x²+y²+z²+2xy+2yz+2xz=100
所以x²+y²+z²
=100-2(xy+xz+yz)
=84
已知x²+y²+z²=xy+yz+xz,求证x=y=z
x²+y²+z²=xy+yz+xz,
所以
2x²+2y²+2z²=2xy+2yz+2xz,
所以
(x-y)^2+(x-z)^2+(y-z)^2=0
所以
x=y=z
希望对你有进步，祝你学业进步，谢谢，望采纳！
已知x+y+z=5,且xy+xz+yz=7,求x²+y²+z²的值
x+y+z=5
∴(x+y+z)²=x²+y²+z²+2xy+2xz+2yx=25
∴x²+y²+z²
=25-2(xy+xz+yz)
=25-2×7
=11
已知x-y=-1,z-y=2,求x²+y²+z²-xy-yz-xz的值
（x²+y²+z²-xy-yz-xz）*2=（x-y）^2+（x-z）^2+（z-y）^2=
（-1）^2+（3）^2+（2）^2=14
14/2=7
(x-y=-1,z-y=2,所以z-x=3)
x／3=y／2＝z／5,求xy+yz+xz／x²+y²+z²
令 x/3=y/2=z/5=k
则 x=3k y=2k z=5k
∴(xy+yz+zx)/(x²+y²+z²)
=(6+10+15)k²/(9+4+25)l²
=31/38
已知x+y+z=2,xy+yz+zx=-5,求x²+y²+z²的值
(x+y+z)^2=4
x^2+y^2+z^2+2xy+2xz+2yz=4
x^2+y^2+z^2+2(-5)=4
x^2+y^2+z^2=14
已知x+y+z=1,x²+y²+z²=2求xy+yz+zx
(x+y+z)²=x²+y²+z²+2xy+2yz+2xz
所以可得：
xy+yz+xz
=[(x+y+z)²-(x²+y²+z²)]/2
=[1²-2]/2
=-1/2
