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先化简再求值:x/y(x+y) -y/x(x+y)其中x=(根号2)+1,y=(根号2)-1
人气:115 ℃ 时间:2020-06-08 22:42:11
解答
原式=x²/[xy(x+y)]-y²/[xy(x+y)]
=(x²-y²)/[xy(x+y)]
=(x+y)/(x-y)/[xy(x+y)]
=(x-y)/(xy)
=[(√2+1)-(√2-1)]/[(√2+1)(√2-1)]
=(√2+1-√2+1)/(√2²-1²)
=2/(2-1)
=2
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