三元一次方程1.已知3x-4Y-Z=0,2X+Y-8Z=0,求(X*X+Y*Y+Z*Z)/(XY+YZ+ZX)的值.2.X+Y+Z=6,X-3Y+2Z=1,3X+2Y-Z=4.求X,Y,Z的值.3.已知4X-5Y+2Z=0,X+4Y-3Z=0(XYZ不等于0),则X比Y比Z的值为()(尽量写出解题过程)

Question

三元一次方程
1.已知3x-4Y-Z=0,2X+Y-8Z=0,求( X*X+Y*Y+Z*Z)/(XY+YZ+ZX)的值.
2.X+Y+Z=6,X-3Y+2Z=1,3X+2Y-Z=4.求X,Y,Z的值.
3.已知4X-5Y+2Z=0,X+4Y-3Z=0(XYZ不等于0),则X比Y比Z的值为( )
(尽量写出解题过程)

Answer 1

(1)(3x-4Y-Z)+4×(2X+Y-8Z)=0
化简得x=3z
代入3x-4Y-Z=0得y=2z
( X*X+Y*Y+Z*Z)/(XY+YZ+ZX)=14z*z/11z*z=14/11
(2)X+Y+Z=6 ①
X-3Y+2Z=1 ②
3X+2Y-Z=4 ③
①+③得 4X+3Y=10 ④
2×①-②得 x+5y=11 ⑤
解 ④⑤组成的二元一次方程组的x=1 y=2
再代入①得z=3
所以x=1 y=2 z=3
(3)4X-5Y+2Z=0 ①
X+4Y-3Z=0 ②
3×①+2×②得14x-7y=0
y=2x
代入①得z=3x x∶y∶z=1∶2∶3