先化简,在求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1先化简,再求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1
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![先化简,在求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1先化简,再求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1](/uploads/image/z/337971-3-1.jpg?t=%E5%85%88%E5%8C%96%E7%AE%80%2C%E5%9C%A8%E6%B1%82%E5%80%BC%EF%BC%9A%28x%2B%E6%A0%B9%E5%8F%B7xy%29%2F%28y%2B%E6%A0%B9%E5%8F%B7xy%29%2B%28%28%E6%A0%B9%E5%8F%B7xy%29-y%29%2F%28x-%E6%A0%B9%E5%8F%B7xy%29%2C%E5%85%B6%E4%B8%ADx%3D%E6%A0%B9%E5%8F%B73%2B1%2Cy%3D%E6%A0%B9%E5%8F%B73-1%E5%85%88%E5%8C%96%E7%AE%80%2C%E5%86%8D%E6%B1%82%E5%80%BC%EF%BC%9A%28x%2B%E6%A0%B9%E5%8F%B7xy%29%2F%28y%2B%E6%A0%B9%E5%8F%B7xy%29%2B%28%28%E6%A0%B9%E5%8F%B7xy%29-y%29%2F%28x-%E6%A0%B9%E5%8F%B7xy%29%2C%E5%85%B6%E4%B8%ADx%3D%E6%A0%B9%E5%8F%B73%2B1%2Cy%3D%E6%A0%B9%E5%8F%B73-1)
先化简,在求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1先化简,再求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1
先化简,在求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1
先化简,再求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1
先化简,在求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1先化简,再求值:(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),其中x=根号3+1,y=根号3-1
(x+根号xy)/(y+根号xy)+((根号xy)-y)/(x-根号xy),
=√x(√x+√y)/√y(√x+√y)+√y(√x-√y)/√x(√x-√y)
=√x/√y+√y/√x=(x+y)/√xy
x=√3+1 y=√3-1 ∴x+y=2√3 xy=2
∴(x+y)/√xy=2√3/2=√3
(x+√xy)/(y+√xy)+(√xy-y)/(x-√xy)
=[(x+√xy)×(x-√xy)+(√xy-y)×(y+√xy)]/[(y+√xy)×(x-√xy)]
=(x²-xy+xy-y²)/(xy+x√xy-y√xy-xy)
=(x²-y²)/[(x-y)√xy]
=(x-y)(x+y)/[(x-y)√xy]
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(x+√xy)/(y+√xy)+(√xy-y)/(x-√xy)
=[(x+√xy)×(x-√xy)+(√xy-y)×(y+√xy)]/[(y+√xy)×(x-√xy)]
=(x²-xy+xy-y²)/(xy+x√xy-y√xy-xy)
=(x²-y²)/[(x-y)√xy]
=(x-y)(x+y)/[(x-y)√xy]
=(x+y)/√xy
=(√3+1+√3-1)/√(√3+1)(√3-1)
=2√3/√2
=√6
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[x+√(xy)]/[y+√(xy)]+[(√(xy)-y]/[x-√(xy)]
=√x(√x+√y)/[√y(√y+√x)]+√y(√x-√y)/[√x(√x-√y)]
=√x/√y+√y/√x
=x/√(xy)+y/√(xy)
=(x+y)/√(xy)
=(√3+1+√3-1)/√[(√3+1)(√3-1)]
=2√3/2
=√3