Question

已知x+y=7,且xy=12,若x<y。求1/x-1/y的值

Answer 1

解：由方程组
{x+y=7
{xy=12
可得
{x=4
{y=3
或{x=3
{y=4
∵x<y
所以x=3,y=4
所以1/x-1/y=1/3-1/4=1/12

Answer 2

1/x-1/y=(y-x)/xy=(y-x)/12
因为（y-x)^2=(y+x)^2-4xy
所以（y-x)^2=7^2-4*12=49-48=1
所以（y-x)=+1或-1
因为x<y 所以y-x=1
所以原式＝1/12

Answer 3

x+y=7=3+4
xy=3*4=12
x<y
x=3，y=4
1/x-1/y
=(y-x)/(xy)
=(4-3)/12
=1/12

Answer 4

(x+y)²-(x-y)²
=(x+y+x-y)(x+y-x+y)
=4xy
则49-(x-y)²=4×12
(x-y)²=1
x<y,x-y<0
所以x-y=-1
y-x=1

所以1/x-1/y
=(y-x)/xy
=1/12

Answer 5

(x+y)^2=49
x^2+ 2xy+ y^2=49
x^2+ 2xy+ y^2-4xy=1
x^2-2xy+ y^2=1
(x-y)^2=1
y-x=正负 1 由于x<y 所以 y-x＝1
1/x-1/y=(y-x)/xy=(y-x)/12＝1/12