已知x:y:z=2:3:4,求x-y-z/3x+2y-z的值.若2x+3y-4z=-3,求3x-4y-z的值
问题描述：
已知x:y:z=2:3:4,求x-y-z/3x+2y-z的值.若2x+3y-4z=-3,求3x-4y-z的值
答
-5/8
答
因为x:y:z=2:3:4,
所以设 x = 2k , y = 3k , z = 4k
所以 (x - y - z)/(3x + 2y - z)
=(2k - 3k - 4k)/(6k + 6k - 4k)
= -5k/8k
= -5/8
若 2x + 3y - 4z = -3
则 4k + 9k - 16z = -3
-3k = -3
k = 1
所以 3x - 4y - z
= 6k - 12k -4k
= -10k
= -10
答
令x=2k,y=3k,z=4k
(x-y-z)/(3x+2y-z)
=(2k-3k-4k)/(3*2k+2*3k-4k)
=-5k/8k
=-5/8
2x+3y-4z=-3
2*2k+3*3k-4*4k=-3
-3k=-3
k=1
3x-4y-z
=3*2k-4*3k-4k
=-10k
=-10*1
=-10