Question

已知X=2+√3，Y=2-√3，求根号X-根号Y分之根号X+根号Y-根号X+根号Y分之根号X-根号Y的值

Answer 1

∵X=2+√3，Y=2-√3
∴x+y=4 x-y=2√3 xy=1
(√X+√y)/(√X-√Y)-(√X-√Y)/(√X+√Y)
=(√X+√y)(√X+√y)/(√X-√Y)(√X+√y)-(√X-√Y)(√X-√Y)/(√X+√Y)(√X-√Y)
=(x+y+2√xy)/(x-y)-(x+y-2√xy)/(x-y)
=6/2√3-2/2√3
=2/√3=2√3/3

Answer 2

(√x+√y)/(√x-√y)=(√x+√y)²/(x-y)=(x+y+2√xy)/(x-y)
x+y=2+√3+2-√3=4
x-y=2+√3-2+√3=2√3
xy=(2+√3)(2-√3)=4-3=1
∴原式=6/2√3=√3

Answer 3

将原式通分有[(√x+√y)^2-(√x-√y)^2]/(x-y)=(4√xy)/(x-y)带入数据得原式=(2√3)/3
本题主要考察分式的变形，及计算能力
要注意多加练习

Answer 4

2√3/3