解方程组 1/x+1/y=7 1/xy=10

解方程组 1/x+1/y=7 1/xy=10
解方程组 1/x+1/y=7 1/xy=10

解方程组 1/x+1/y=7 1/xy=10
构造一元二次方程m^2-7m+10=0,则1/x,1/y是它的两个根
很容易解得m=2,m=5
因此x=1/2,y=1/5,或x=1/5,y=1/2

X1=1/5
x2=1/2

1/y = 7 - 1/x
1/x * (7 - 1/x) = 10
(1/x)^2 - 7/x + 10 = 0
(1/x - 2)(1/x - 5) = 0
1/x = 2, 1/x = 5
x = 1/2, 1/5

1/x+1/y=7 ①1/xy=10②
由②可得xy=1/10③
③×①可得x+y=0.7
则y=0.7-x④
④代入③可得x(0.7-x)=0.1⑤
解⑤得x1=0.2 x2=0.5
则y1=0.5 y2=0.2

1/xy=10,xy=0.1
1/x+1/y=（x+y）/xy=10(x+y)=7,x+y=0.7,y=0.7-x,代入上式，得：x(0.7-x)=0.1
x^2-0.7x+0.1=0,
(x-0.2)(x-0.5)=0
x1=0.2,y1=0.7-x1=0.5;
x2=0.5,y2=0.7-x2=0.2