解x(x+y+z)=4-yz、y(x+y+z)=9-xz、z(x+y+z)=25-xy方程组
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![解x(x+y+z)=4-yz、y(x+y+z)=9-xz、z(x+y+z)=25-xy方程组](/uploads/image/z/2108729-65-9.jpg?t=%E8%A7%A3x%28x%2By%2Bz%29%3D4-yz%E3%80%81y%28x%2By%2Bz%29%3D9-xz%E3%80%81z%28x%2By%2Bz%29%3D25-xy%E6%96%B9%E7%A8%8B%E7%BB%84)
解x(x+y+z)=4-yz、y(x+y+z)=9-xz、z(x+y+z)=25-xy方程组
解x(x+y+z)=4-yz、y(x+y+z)=9-xz、z(x+y+z)=25-xy方程组
解x(x+y+z)=4-yz、y(x+y+z)=9-xz、z(x+y+z)=25-xy方程组
(一)x(x+y+z)=4-yz.===>x²+(y+z)x+yz=4.===>(x+y)(x+z)=4①.同理,将后面两个方程变形可得(x+y)(y+z)=9,②(x+z)(y+z)=25.③,将三个方程相乘可得(x+y)(y+z)(x+z)=±30.④.(二)当(x+y)(y+z)(x+z)=30时,与前面三个方程相除得y+z=15/2.x+z=10/3.x+y=6/5.这三个方程相加得x+y+z=361/60.再与前面三个方程先将得:x=-89/60.y=161/60.z=289/60.(三)当(x+y)(y+z)(z+x)=-30时,同理可解.