解x(x+y+z)=4-yz、y(x+y+z)=9-xz、z(x+y+z)=25-xy方程組

數(shù)學(xué)人氣：932 ℃時(shí)間：2020-06-24 00:53:27

優(yōu)質(zhì)解答

（一）x(x+y+z)=4-yz.===>x²+(y+z)x+yz=4.===>(x+y)(x+z)=4①.同理,將后面兩個(gè)方程變形可得(x+y)(y+z)=9,②(x+z)(y+z)=25.③,將三個(gè)方程相乘可得(x+y)(y+z)(x+z)=±30.④.(二）當(dāng)(x+y)(y+z)(x+z)=30時(shí),與前面三個(gè)方程相除得y+z=15/2.x+z=10/3.x+y=6/5.這三個(gè)方程相加得x+y+z=361/60.再與前面三個(gè)方程先將得:x=-89/60.y=161/60.z=289/60.(三）當(dāng)(x+y)(y+z)(z+x)=-30時(shí),同理可解.