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
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