x+y/2=z+x/3+y=z/4,...x+y+z=27.解方程组.X+Y/2=Z+X/3=Y+Z/4,X+Y+Z=27.解方程

问题描述:

x+y/2=z+x/3+y=z/4,...x+y+z=27.解方程组.
X+Y/2=Z+X/3=Y+Z/4,X+Y+Z=27.解方程

X+Y/2=Z+X/3(1)整理得2x/3=z-y/2(3)
X+Y/2=Y+Z/4(2)整理得x=y/2+z/4(4)
(3)+(4)得5x/3=5z/4,所以x=3z/4(5)
由Z+X/3=Y+Z/4得3z/4=y-x/3
把x=3z/4代入3z/4=y-x/3得x=3y/4
X+Y+Z=27
∴y=z=108/11
x=81/11

X+Y/2=Z+X/3→6X+3Y=6Z+2X→4X+3Y=6Z ①
Z+X/3=Y+Z/4→12Z+4X=12Y+3Z→4X-12Y=-9Z ②
X+Y/2=Y+Z/4→4X+2Y=4Y+Z→4X-2Y=Z ③
1-2得:15Y=15Z Y=Z
代入3 得:4X-3Y=0 ④
X+Y+Z=X+2Y=27 ⑤
解4.5得:......接下来你自己做了

设(x+y)/2=(x+z)/3=(y+z)/4=k则x+y=2k x+z=3k y+z=4k 代入x+y+z=272k+3k+4k=27 k=3所以 x+y= 6 (1)x+z=9 (2)y+z=12 (3)(1)+(2)+(3) 2(x+y+z)=27 x+y+z=27/2 (4)(4)-(1) z=15/2(4)-(2) y=9/2(4)-(3) x=3/2即为所求...