已知x=2+根号3,y=2-根号3,求代数式[(x+y):(x-y)-(x-y):(x+y)]*(1:x²)-(1:y²) 的值代数式图片

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已知x=2+根号3,y=2-根号3,求代数式[(x+y):(x-y)-(x-y):(x+y)]*(1:x²)-(1:y²) 的值代数式图片

已知x=2+根号3,y=2-根号3,求代数式[(x+y):(x-y)-(x-y):(x+y)]*(1:x²)-(1:y²) 的值代数式图片
已知x=2+根号3,y=2-根号3,求代数式[(x+y):(x-y)-(x-y):(x+y)]*(1:x²)-(1:y²) 的值
代数式图片

已知x=2+根号3,y=2-根号3,求代数式[(x+y):(x-y)-(x-y):(x+y)]*(1:x²)-(1:y²) 的值代数式图片
[(x+y):(x-y)-(x-y):(x+y)]*(1:x²)-(1:y²)
=[(x+y)²-(x-y)²]/(x²-y²) ×(y²-x²)/(x²y²)
=4xy/(x²y²)
=4/(xy)
=4/[(2+√3)(2-√3)]
=4/(4-3)=4
前面因式通分:
(x+y):(x-y)-(x-y):(x+y)= (x+y)²/[(x-y)(x+y)]-(x-y)²/[(x+y)(x-y)]
=[(x+y)²-(x-y)²]/(x²-y²)

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