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Question Number 61343 by bhanukumarb2@gmail.com last updated on 01/Jun/19

Answered by MJS last updated on 01/Jun/19

$$x=a-\frac{1}{a-\frac{1}{a-...}}$$$$x=a-\frac{1}{x}$$$$x^2-ax+1=0$$$$x=\frac{a}{2}\pm \frac{\sqrt{a^2-4}}{2}$$$$a=2207\Rightarrow x=\frac{2207\pm 987\sqrt{5}}{2}$$$$\sqrt[8]{\frac{2207\pm 987\sqrt{5}}{2}}=\sqrt{\sqrt{\sqrt{\frac{2207\pm 987\sqrt{5}}{2}}}}$$$$\mathrm{step}1$$$${(a\pm b\sqrt{5})}^2=\frac{2207\pm 987\sqrt{5}}{2}\Rightarrow a=\frac{47}{2},b=\frac{21}{2}$$$$\mathrm{step}2$$$${(a\pm b\sqrt{5})}^2=\frac{47\pm 21\sqrt{5}}{2}\Rightarrow a=\frac{7}{2},b=\frac{3}{2}$$$$\mathrm{step}3$$$${(a\pm b\sqrt{5})}^2=\frac{7\pm 3\sqrt{5}}{2}\Rightarrow a=\frac{3}{2};b=\frac{1}{2}$$$$\mathrm{result}\mathrm{is}$$$$\frac{3\pm \sqrt{5}}{2}$$

Commented by bhanukumarb2@gmail.com last updated on 01/Jun/19

$$thankssir$$

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