世界名題

x(x+y+z)=12-yz
y(x+y+z)=15-zx
z(x+y+z)=20-xy
解聯立求x,y,z

原連結

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Lu-chun Chen 解出

x(x+y+z)=12-yz
y(x+y+z)=15-zx
z(x+y+z)=20-xy

x^2+xy+xz+yz=12
y^2+xy+yz+zx=15
z^2+zx+yz+xy=20

(x+y)(z+x)=12
(y+z)(x+y)=15
(z+x)(y+z)=20

(x+y)(y+z)(z+x)=60　v　-60

(1)
x+y=3
y+z=5
z+x=4

x+y+z=6

x=1,y=2, z=3

(2)
x+y=-3

y+z=-5

z+x=-4

x+y+z=-6
x=-1,y=-2,z=-3