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# Help

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What is the value of  for which $$\sqrt{x + \sqrt{x + \sqrt{x + \ldots}}} = 5?$$

Jan 12, 2021

#1
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Let $y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}=5.$

If you square $y$, you get $25=x+\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}=x+y$.

But since the value of y is 5, then you get $25=x+5$.

Therefore, $x=\boxed{20}$.

Jan 12, 2021

#1
+2
Let $y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}=5.$
If you square $y$, you get $25=x+\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}=x+y$.
But since the value of y is 5, then you get $25=x+5$.
Therefore, $x=\boxed{20}$.