已知2x-3y+z=0且3x-2y-6z=0,求(x눀+y눀+z눀)⼀(2x눀+y눀-z눀)的值

2025-01-06 02:35:26
推荐回答(2个)
回答1:

设z=1
2x-3y=-1 (1)
3x-2y=6 (2)
(1)+(2)
x-y=1
则代入(1)
2-y=-1
y=3,x=4
(x²+y²+z²)/(2x²+y²-z²)
=(12+9+1)/(32+9-1)
=22/40
=11/20

回答2:

2x-3y+z=0 (1)
3x-2y-6z=0 (1)
(1)×2-(2)×3
-5x+20z=0
z=x/4

(1)×6+(2)
15x-20y=0
y=3x/4

原式=(x²+9x²/16+x²/16)/(2x²+9x²/16-x²/16)
=(13x²/8)/(5x²/2)
=13/20