+26367 If
\(\sqrt{x+\!\sqrt{x+\!\sqrt{x+\!\sqrt{x+\cdots}}}}=10\)
solve for x.
My attempt:
\(\begin{array}{|rcll|} \hline y &=& \sqrt{x+\!\sqrt{x+\!\sqrt{x+\!\sqrt{x+\cdots}}}} \\ y &=& \sqrt{x+\!y} \quad | \quad \text{square both sides} \\ y^2 &=& x+y \quad | \quad y = 10 \\ 100 &=& x + 10 \\ \mathbf{x} &=& \mathbf{90} \\ \hline \end{array}\)
