YLL討論網

由 **lskuo** 於星期二一月 28, 2014 11:33 am

Anonymous 寫到:x=2+sqrt(3+sqrt(2+sqrt(3+sqrt(2+3sqrt(2+sqrt(....))))))>2
=>x=2+sqrt(3+x)
=>x^2-4x+4=3+x
=> x^2-5x+4=0=(x-4)(x-1)=>x=4 or 1; 取x=4...ans

第二步有誤：應是
x = 2 + sqrt(3 + sqrt(x) )

再者，從題目本身應可判斷 x < 2 + sqrt(4) = 4

由訪客於星期日一月 26, 2014 11:19 am

x=2+sqrt(3+sqrt(2+sqrt(3+sqrt(2+3sqrt(2+sqrt(....))))))>2
=>x=2+sqrt(3+x)
=>x^2-4x+4=3+x
=> x^2-5x+4=0=(x-4)(x-1)=>x=4 or 1; 取x=4...ans

由訪客於星期三十一月 06, 2013 2:00 pm

2+根號{3+根號[2+根號(3+...)]}=?

(請將產生的程式碼，剪貼至上方文章區！)
[quote="Anonymous"]x=2+sqrt(3+sqrt(2+sqrt(3+sqrt(2+3sqrt(2+sqrt(....))))))>2 =>x=2+sqrt(3+x) =>x^2-4x+4=3+x => x^2-5x+4=0=(x-4)(x-1)=>x=4 or 1; 取x=4...ans[/quote]