+0  
 
0
78
1
avatar

If \(\sqrt{x+\!\sqrt{x+\!\sqrt{x+\!\sqrt{x+\cdots}}}}=10\) solve for x.

 Jan 21, 2021
 #1
avatar+25640 
+1

If
\(\sqrt{x+\!\sqrt{x+\!\sqrt{x+\!\sqrt{x+\cdots}}}}=10\)
solve for x.

 

My attempt:

 

\(\begin{array}{|rcll|} \hline y &=& \sqrt{x+\!\sqrt{x+\!\sqrt{x+\!\sqrt{x+\cdots}}}} \\ y &=& \sqrt{x+\!y} \quad | \quad \text{square both sides} \\ y^2 &=& x+y \quad | \quad y = 10 \\ 100 &=& x + 10 \\ \mathbf{x} &=& \mathbf{90} \\ \hline \end{array}\)

 

laugh

 Jan 21, 2021

52 Online Users

avatar
avatar
avatar