Question

两道高一数学题，帮我解一下，写一下过程，谢谢

1.已知X>0,Y>0,且√X(√x+√y)=3√y(√x+5√y),求（2x+(√xy)+3y）／（x+(√xy)－y）
的值？
2.已知a^2n=√2+1，求（a^3n+a^-3n）/（a^n+a^-n）的值（其中n∈N）
急啊！！！！！！！！各位帮帮我啊！！！！谢谢了！！！！！快~~

Answer 1

X(√x+√y)=3√y(√x+5√y)
=>x+√(xy)-3√(xy)-15y=0
=>(√x-5√y)(√x+3√y)=0
x>0,y>0=>√x+3√y>0
=>√x-5√y=0 =>x=25y
=>(2x+(√xy)+3y）/(x+(√xy)－y)
=(50y+5y+3y)/(25y+5y-y)
=2

(a^3n+a^-3n)/（a^n+a^-n）
=a^(2n)-1+a^(-2n)=√2+1-1+1/(√2+1)=2√2-1

追问

真的太谢谢了！！我会了！！O(∩_∩)O~再问你一个我不确定的题好吧？？
已知x^1/2+x^-1/2=3,求（x^3/2+x^-3/2－3）/（x^2-x^-2－2）的值。

Answer 2

√X(√x+√y)=3√y(√x+5√y)
√X*√x+√X*√y=3√y*√x+√y*15√y
x+√(xy)=3√(xy)+15y
x-2√(xy)=15y
x-2√(xy)+y=16y
(√x-√y)^2=16y
√x-√y=4√y
√x=5√y
x=25y
[2x+(√xy)+3y)]／[x+(√xy)－y]
=[2*25y+√(25y*y)+3y]/[25y+√(25y*y)-y]
=(50y+5y+3y)/(25y+5y-y)
=58y/29y
=2

（a^3n+a^-3n）/（a^n+a^-n）
=(a^n+a^-n)(a^2n+a^-2n-1)/(a^n+a^-n)
=a^2n+a^-2n-1
=√2+1-1+1/(√2+1)
=√2 +√2+1
=2√2-1

x^1/2+x^-1/2=3,求（x^3/2+x^-3/2－3）/（x^2-x^-2－2）

x^1/2+x^-1/2=3
(x^1/2+x^-1/2)^2=9
x^1+x^-1+2=9
x^1+x^-1=7

x^1+x^-1=7
x^1-2+x^-1=7-2
(x^1/2-x^-1/2)^2=5
(x^1/2-x^-1/2)^2=5
x^1/2-x^-1/2=±√5

当x^1/2-x^-1/2=√5，x^1+x^-1=7时
（x^3/2+x^-3/2－3）/（x^2-x^-2－2）
=[(x^1/2+x^-1/2)(x+x^-1-1)-3]/[(x^1+x^-1)(x^1-x^-1)-2]
=[3*(7-1)-3]/[7(x^1/2+x^-1/2)(x^1/2-x^-1/2)-2]
=15/[7*3*(x^1/2-x^-1/2)-2]
=5/[7*(x^1/2-x^-1/2)-2]
=5/[7*√5-2]
=5/(7√5-2)
=5(7√5+2)/(7√5-2)(7√5+2)
=(35√5+10)/241

当x^1/2-x^-1/2=-√5，x^1+x^-1=7时
（x^3/2+x^-3/2－3）/（x^2-x^-2－2）
=[(x^1/2+x^-1/2)(x+x^-1-1)-3]/[(x^1+x^-1)(x^1-x^-1)-2]
=[3*(7-1)-3]/[7(x^1/2+x^-1/2)(x^1/2-x^-1/2)-2]
=15/[7*3*(x^1/2-x^-1/2)-2]
=5/[7*(x^1/2-x^-1/2)-2]
=5/[7*(-√5)-2]
=-5/(7√5+2)
=-5(7√5-2)/(7√5-2)(7√5+2)
=(10-35√5)/241

追问

真的太谢谢了！！我会了！！O(∩_∩)O~再问你一个我不确定的题好吧？？
已知x^1/2+x^-1/2=3,求（x^3/2+x^-3/2－3）/（x^2-x^-2－2）的值。