#### Multiple Choice Question (MCQ)

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

1. ×

\dfrac{\sqrt{7}+1 }{2}

2. ×

\dfrac{\sqrt{6}+1 }{2}

3. \dfrac{\sqrt{5}+1 }{2}

4. ×

\dfrac{\sqrt{5}-1 }{2}

Collected in the board: Square Root

Steven Zheng posted 2 weeks ago

1. 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