x、y、z满足4x-3y-6z=0,x+2y-7z=0求（2x^2+3y^2+6z^2）/(x^2+5y^2+7x^2)已知xyz=1求x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)的值是多少?A＝333/4444B＝4444/55555那个大?第一题打错了！应是x、y、z满足4x-3y-6z=0,x+2y-7z=0求（

Question

x、y、z满足 4x-3y-6z=0 ,x+2y-7z=0
求（2x^2+3y^2+6z^2）/(x^2+5y^2+7x^2)
已知xyz=1 求 x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1) 的值是多少?
A＝333/4444 B＝4444/55555 那个大?
第一题打错了！应是
x、y、z满足 4x-3y-6z=0 ,x+2y-7z=0
求（2x^2+3y^2+6z^2）/(x^2+5y^2+7z^2)

Answer 1

1. 4x-3y-6z=0 , x+2y-7z=0
解得 x=3z, y=2z
2x^2+3y^2+6z^2=2*9z^2+3*4z^2+6z^2=36z ^2
x^2+5y^2+7z^2=9z^2+5*4z^2+7z^2=36z^2
（2x^2+3y^2+6z^2）/(x^2+5y^2+7z^2)
=1
2.xyz=1
x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)
=x/(xy+x+xyz)+y/(yz+y+1)+yz/(xyz+yz+y)
=1/(yz+y+1)+y/(yz+y+1)+yz/(yz+y+1)
=1
3.A=333/4444=3/4（111/1111）
B=4444/55555 =4/5（1111/11111）
所以A/B=（5*3/4*4）*（11111*111/1111^2)
=15/16*(11111*111/1111^2)