Question

tim \(x=\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+....}}}}}\)

Answer 1

\(x=\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+....}}}}}\)

\(\Rightarrow x^2=5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+...}}}}\)

\(\Rightarrow x^4=25+10\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+....}}}}+13+\sqrt{5+\sqrt{13+\sqrt{5+...}}}\)

\(\Leftrightarrow x^4=38+10x^2+x\)

\(\Leftrightarrow x^4-10x^2-x-38=0\)

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