解方程组:{x(x+y+z)=6 {y(x+y+z)=9 {z(x+y+z)=10

问题描述:

解方程组:{x(x+y+z)=6 {y(x+y+z)=9 {z(x+y+z)=10

设x+y+z≠0则x(x+y+z)=6 (1)y(x+y+z)=9 (2)z(x+y+z)=10 (3)(1)/(2)得:x/y=2/3(3)/(1)得:z/x=5/3(2)/(3)得:y/z=9/10x=2/3y,z=10/9y代入(1)得y(2/3y+y+10/9y)=9y=±9/5当y=9/5时,x=6/5,z=2...