Question

大家帮帮忙啊，谢谢了。

Answer 1

数理答疑团为您解答，希望对你有所帮助。

(1)原式=（√x +√y）²/[(√x -√y)(√x +√y)] - （√x -√y）²/[(√x +√y)(√x -√y)]
=[（√x +√y）²- （√x -√y）²]/[(√x -√y)(√x +√y)]
=（2√x 2√y）/(x -y)
=4√(x y)/(x -y)
=4√(1/3 * 2/5)/(1/3 -2/5)
=-4√30
(2)题意可知：a+b=8，ab=10，a-b=2√（8²-4*1*10）=4√6
（√a -√b）/(√a +√b)
=（√a -√b）²/(a -b)
=（a+b-2√ab）/(a -b)
=（8-2√10）/(4√6) 分子分母同乘√6
=（2√6 - √15）/6

祝你学习进步，更上一层楼！ (*^__^*)

Answer 2

(√x+√y)/(√x-√y)-(√x-√y)/(√x+√y)
=(√x+√y)²/(x-y)-(√x-√y)²/(x-y)
=[(√x+√y)²-(√x-√y)²]/(x-y)
=[(x+2√(xy)+y)-(x-2√(xy)+y)]/(x-y)
=(x+2√(xy)+y-x+2√(xy)-y)/(x-y)
=[2√(xy)+2√(xy)]/(x-y)
=4√(xy)/(x-y)
=4√(1/3*2/5)/(1/3-2/5)
=4√(2/15)/(5/15-6/15)
=4√(30/225)/(-1/15)
=-4√30/15*(15)
=-4√30