Question

若x>0,y>0,且√x(√x+√y)=3√y(√x+5√y),求2x+2√x*√y+3y/x-√x*√y+y

Answer 1

√x(√x+√y)=3√y(√x+5√y)

x+√xy=3√xy+15y

x-2√xy-15y=0

(√x-5√y)(√x+ 3√y)=0

因为x,y为正数

所以√x-5√y=0 √x=5√y

x=25y

（2x+√xy+3y）/(x+√xy-y)

=（50y+5y+3y）/(25y+5y-y)

=58/29