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


Answer

  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

    Solving the quadratic equation gives

    x = \dfrac{\sqrt{5}+1 }{2}

    Therefore C is the answer


Steven Zheng posted 2 weeks ago

Scroll to Top