Question

已知x=2+√3,y=2-√3,求(x-y分之x+y-x+y分之x-y)*(x2分之1-y2分之1)的值

Answer 1

x=2+√3,y=2-√3
那么：x+y=4
xy=4-3=1
x-y=2√3

(x-y分之x+y-x+y分之x-y)*(x2分之1-y2分之1)
=((x+y)²-(x-y)²)/(x²-y²) * （y²-x²)/x²y²
=-(4xy)/x²y²
=-4/xy
=-4

追问

万谢万谢！

追答

答案肯定是负的，

Answer 2

(x-y分之x+y-x+y分之x-y)*(x2分之1-y2分之1)
=[(x+y)²-(x-y)²]/(x+y)(x-y)×(x²-y²)/x²y²
=4xy/(x²-y²)×(x²-y²)/x²y²
=4/(xy)
=4/(2+√3)(2-√3)
=4