已知:x=根号3+1,y=根号3-1,求x^2-2xy+y^2分之x^2-y^2

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已知:x=根号3+1,y=根号3-1,求x^2-2xy+y^2分之x^2-y^2
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已知:x=根号3+1,y=根号3-1,求x^2-2xy+y^2分之x^2-y^2
已知:x=根号3+1,y=根号3-1,求x^2-2xy+y^2分之x^2-y^2

已知:x=根号3+1,y=根号3-1,求x^2-2xy+y^2分之x^2-y^2
x=√3+1,y=√3-1
x-y=√3+1-√3+1=2
x+y=√3+1+√3-1=2√3
∴ ﹙x²-y²﹚/﹙x²-2xy+y²﹚
=﹙x-y﹚﹙x+y﹚/﹙x-y﹚²
=﹙x+y﹚/﹙x-y﹚
=2√3/2
=√3.

(x²-y²)/(x²-2xy+y²)
=(x+y)(x-y)/(x-y)²
=(x+y)/(x-y)
当x=根号3+1,y=根号3-1时
原式=(√3+1+√3-1)/(√3+1-√3+1)=2√3/2=√3
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x=√3+1,y=√3-1
(x^2-y^2)/(x^2-2xy+y^2)
=(x-y)(x+y)/(x-y)^2
=(x+y)/(x-y)
=(√3+1+√3-1)/[√3+1-(√3-1)]
=2√3/[√3+1-√3+1)
=2√3/2
=√3

(x^2-2xy+y^2)/(x^2-y^2)=(x-y)^2/(x-y)(x+y)=(x-y)/(x+y)=(根号3+1-根号3+1)/(根号3+1+根号3-1)=2/2根号3=1/根号3
=根号3/3

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