由 danny 於 星期五 七月 19, 2013 3:32 am
√ (x+1/x+1)+√ (x+1/x)=x ...(1)
let √ (x+1/x+1)-√ (x+1/x)=y
xy= (x+1/x+1)- (x+1/x)=1
so y=1/x ,we have √ (x+1/x+1)-√ (x+1/x)=1/x ...(2)
(1)+(2)=> 2√ (x+1/x+1)=x+1/x , wlog x+1/x=k
k=2√ (k+1) => k=2 ± 2√ 2 ,since k =√ (x+1/x) > 0
k=2+2√ 2=x+1/x => x=(1+√ 2)±√[2(1+√ 2)]