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Question-158919




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

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