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Simplify $\sqrt{420 - \sqrt{420 - \sqrt{420 - \sqrt{420 - \dotsb}}}}$.

 Mar 31, 2021

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 #1
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\(x=\sqrt{420 - \sqrt{420 - \sqrt{420 - \sqrt{420 - \dotsb}}}}\\x^2=420-x\\x^2+x-420=0\\(x-20)(x+21)=0\\\boxed{x=20}\)

lol

 Mar 31, 2021
 #1
avatar+420 
+1
Best Answer

\(x=\sqrt{420 - \sqrt{420 - \sqrt{420 - \sqrt{420 - \dotsb}}}}\\x^2=420-x\\x^2+x-420=0\\(x-20)(x+21)=0\\\boxed{x=20}\)

lol

textot Mar 31, 2021

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