一道初二数学题
已知xy=1,x=2+√3,求1/(x+1)+1/(y-1)的值
参考答案:因为xy=1,x=2+√3
y=1/x=2-√3
1/(x+1)+1/(y-1)
=(y-1+x+1)/[(x+1)(y-1)]
=(x+y)/(xy-x+y-1)
=(2+√3+2-√3)/(1-2-√3+2-√3-1)
=4/(-2√3)
=-2/√3
=-(2/3)√3
已知xy=1,x=2+√3,求1/(x+1)+1/(y-1)的值
参考答案:因为xy=1,x=2+√3
y=1/x=2-√3
1/(x+1)+1/(y-1)
=(y-1+x+1)/[(x+1)(y-1)]
=(x+y)/(xy-x+y-1)
=(2+√3+2-√3)/(1-2-√3+2-√3-1)
=4/(-2√3)
=-2/√3
=-(2/3)√3