Question

怎么解方程组 {2/x + 3/y =1/4 1 - 4/x = (x+2)/y

八年级解法

Answer 1

1)2/x+3/y=1/4
8y+12x=xy
8y-xy=-12x
y(8-x)=12x
y=(-12x)/(8-x)

2)y-4y/x=x+2
xy-4y=cx((-12x)/(8-x))-4((-12x)/(8-x))=x^2+2x
-12x^2+48x=8x^2+16x-x^3-2x^2
x^3-18x^2+32x=0
x^2-18x+32=0
(x-16)(x-2)=0
x=16,x=2
y=24,y=-4

Answer 2

{2/x + 3/y =1/4 ①
1 - 4/x = (x+2)/y ②
x≠0，y≠0
由 ①式得y=12x/(x-8) x ≠ 8 代入②式化简得
x²-18x+32=0
x1=2，x2=16
y1=-4，y2=24