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Question Number 144474 by SOMEDAVONG last updated on 26/Jun/21

$$\mathrm{A}=\sqrt{1+\sqrt{7+\sqrt{1+\sqrt{7+\sqrt{1+\sqrt{7+...........}}}}}}$$

Answered by mr W last updated on 25/Jun/21

$$x=\sqrt{1+\sqrt{7+x}}$$$${(x^2-1)}^2=7+x$$$$x^4-2x^2-x-6=0$$$$(x-2)(x^3+2x^2+2x+3)=0$$$$\Rightarrow x=2>0$$

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