Question Number 158919 by quvonnn last updated on 10/Nov/21
Answered by floor(10²Eta[1]) last updated on 10/Nov/21
$$\mathrm{4x}=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\mathrm{4x}}}}=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+…}}}}} \\ $$$$\mathrm{4x}=\sqrt{\mathrm{x}+\mathrm{4x}}=\sqrt{\mathrm{5x}} \\ $$$$\mathrm{16x}^{\mathrm{2}} =\mathrm{5x}\Rightarrow\mathrm{x}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\frac{\mathrm{5}}{\mathrm{16}} \\ $$$$ \\ $$