MQ22 --- Fraction Operation

To Copestone,

這條是分子無開頭, 分母無結尾的, 不是"無開頭, 又無結尾的".

2012-06-16 10:04:16 補充：
Let p = (((.../x + x)/x + x)/x + x)
==> p/x + x = p
==> p + x² = px
==> p = x²/(x - 1)

Let q = (x + x/(x + x/(x + x/...)))
==> x + x/q = q
==> x/q² + x/q - 1 = 0
==> 1/q = [-x ± √(x² + 4x)]/(2x)

(((.../x + x)/x + x)/x + x)/(x + x/(x + x/(x + x/...)))
= p/q
= [x²/(x - 1)] * [-x ± √(x² + 4x)]/(2x)
= x[x ± √(x² + 4x)]/[2(1 - x)]

y=(((.../x + x)/x + x)/x + x)
x(y-x)=y
y=x²/(x-1)
z=(x + x/(x + x/(x + x/...)))
z-x=x/z
z²-xz-x=0
z=[x±√(x²+4x)]/2
(((.../x + x)/x + x)/x + x)/(x + x/(x + x/(x + x/...)))
=y/z
=2x²/(x-1)[x±√(x²+4x)]

2012-06-16 12:06:15 補充：
=2x²[x-(±√(x²+4x))] /(x-1)[x±√(x²+4x)] [x-(±√(x²+4x))]
=2x²[x-(±√(x²+4x))]/(-4x)(x-1)
=x[-x±√(x²+4x)]/2(x-1)

求不到 (x + x/(x + x/(x + x/...)))