Question

1.已知X>0,Y>0,且√X(√x+√y)=3√y(√x+5√y),求（2x+(√xy)+3y）／（x+(√xy)－y

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