λ=√(9・12・12+4)/12＝√1300/12の場合を考える。

12x^2+bx+c=0

の正の解が

{-b+√(9・12・12+4)}/24であるから、

b^2-48c=1300＞b^2

b,cは負数とするとc=[1,27]

b=-34,c=-3

b=-26,c=-13***

b=-22,c=-17

b=-14,c=-23

b=-10,c=-25

b=-2,c=-27

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29x^2-63x-31

9a^2-4=7565

b^2-116c=7565,c=[1,65]

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169x^2-367x-181

9a^2-4=257045

b^2-676c=257045,c=[1,380]

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194x^2-432x-196

9a^2-4=338720

b^2-776c=338720,c=[1,436]

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√5/1→x^2-x-1

√8/2→x^2-2x-1

√221/5→5x^2-11x-5

√1517/13→13x^2-29x-13

√7565/29→29x^2-63x-31・・・ペル

√10400/34→17x^2-38x-17

√71285/89→89x^2-199x-89

√257045/169→169x^2-367x-181・・・ペル

√338720/194→97x^2-216x-98・・・どちらでもない

√488597/233→233x^2-521x-233

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λ>3に対して

√13/1→x^2-3x-1=0

√85/3→3x^2-7x-3=0

√580/8→8x^2-18x-8=0=0

√3973/21→21x^2-47x-21=0

√27229/55→55x^2-123x-55=0

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12x^2-26x-13=0

x={+26+√ (1300)}/24+++

x=3+{-46+√ (1300)}/24・・・{-46+√ (1300)}が負になる

12x^2-22x-17=0

x={22+√ (1300)}/24+++

x=3+{-72+√ (1300)}/24・・・{-72+√ (1300)}が負になる

12x^2-34x-3=0

x={34+√ (1300)}/24+++

x=3+{-38+√ (1300)}/24・・・{-38+√ (1300)}が負になる

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huninaru

x=3+1/(97/{-86+√ (1300)})

x=3+1/({86+√ (1300)}/142)

x=3+1/(1+{-56+√ (1300)}/142)

x=3+1/(1+1/(142/{-56+√ (1300)})

x=3+1/(1+1/({56+√ (1300)}/127)

x=3+1/(1+1/(1+{-71+√ (1300)}/127)

x=3+1/(1+1/(1+1/(127/{-71+√ (1300)})

x=3+1/(1+1/(1+1/({71+√ (1300)}/127)

x=3+1/(1+1/(1+1/(1+{-56+√ (1300)}/127)

x=3+1/(1+1/(1+1/(1+1/(127/{-56+√ (1300)})

x=3+1/(1+1/(1+1/(1+1/({56+√ (1300)}/142)

x=3+1/(1+1/(1+1/(1+1/(1+{-86+√ (1300)}/142)

x=3+1/(1+1/(1+1/(1+1/(1+1/(142/{-86+√ (1300)})

x=3+1/(1+1/(1+1/(1+1/(1+1/({86+√ (1300)}/97)

x=3+1/(1+1/(1+1/(1+1/(1+1/(2+{-108+√ (1300)}/97)+++

x=3+1/(1+1/(1+1/(1+1/(1+1/(2+1/(97/{-108+√ (1300)})

x=3+1/(1+1/(1+1/(1+1/(1+1/(2+1/({108+√ (1300)}/98))

x=3+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+{-88+√ (1300)}/98))

x=3+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(98/{-88+√ (1300))})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/{88+√ (21170)}/137)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+{-49+√ (21170)}/137)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(137/{-49+√(21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/{49+√ (21170)})/137}

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+{-88+√ (21170)})/137}

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(137/{-88+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/({88+√(21170)}/98)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+{-108+√(21170)}/98)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(98/{-108+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/({108+√ (21170)}/97)++++

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+{-86+√ (21170)}/97)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(97/{-86+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/({86+√(21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+{-56+√ (21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(142/{-56+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/({56+√(21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+{-71+√(21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(127/{-71+√(21170)}

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/({71+√(21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+{-56+√(21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(127/{-56+√(21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(56+√(21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(1+{-86+√(21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(1+1/(142/{-86+√(21170)}

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(1+1/({86+√(21170)}/97)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(1+1/(2+(-108+√(21170)}/97}+++

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x=[2:1,1,1,1,2,2,1,1,2---,2,1,1,1,1,2,2,1,1,2,・・・]={108+√ (21170)}/97

y={-108+√ (21170)}/97=[0:2,1,1,2,2,1,1,1,1,2,---,2,1,1,2,2,1,1,1,1,2

y=1/(2+1/(1+1/(1+1/(2+1/x)

=1/(2+1/(1+1/(1+x/(2x+1)

=1/(2+1/(1+(2x+1)/(3x+1)

=1/(2+(3x+1)/(5x+2)

=(5x+2)/(13x+5)

y=

(734+5√ (21170)/(1889+13√(21170))

(734+5√ (21170)(1889-13√(21170)))/(3568321-3577730)

(1386526-1376050-97√ (21170))/(-9409)

(-108+√ (21170))/(97)・・・OK

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