已知X=根号2减1,Y=根号2加1,求Y分之X+X分之Y的值

题目

已知X=根号2减1,Y=根号2加1,求Y分之X+X分之Y的值

答案

x/y+y/x
=(x²+y²)/xy
=[(x+y)²-2xy]/xy
=(x+y)²/xy-2
=(√2-1+√2+1)²/(√2-1)(√2+1)-2
=8-2
=6