已知x+y+z=5,且xy+xz+yz=7,求x²+y²+z²的值

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已知x+y+z=5,且xy+xz+yz=7,求x²+y²+z²的值

已知x+y+z=5,且xy+xz+yz=7,求x²+y²+z²的值
已知x+y+z=5,且xy+xz+yz=7,求x²+y²+z²的值

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

(x+y+z)²=x²+y²+z²+2xy+2xz+2yz
5²=x²+y²+z²+2(xy+xz+yz)
25=2×7+x²+y²+z²
x²+y²+z²=25-14
x²+y²+z²=11