If $$x=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\infty}}}} $$, then the value of $$x$$ is

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Uniteasy Admin · Accepted Answer

If $$x=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\infty}}}} $$, the radical part under the first radical is also equal to $$x$$. Then we get the following equation.
$$x=\sqrt{1+x}  $$
$$x^2-x-1=0$$
Solving the quadratic equation gives
$$x = \dfrac{\sqrt{5}+1  }{2}  $$
Therefore C is the answer

Multiple Choice Question (MCQ)

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