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Solve for x:

\(x = \sqrt{x^2 + \sqrt{2020-\sqrt{x^2 + \sqrt{2020 - \sqrt{x^2 + 2020 - \sqrt{\cdots}}}}}}\)

 Dec 20, 2019
 #1
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Subbing the expression  for x  into the radical, we have that

 

x = √[  x^2 +  √[2020 - x ] ]      square both sides

 

x^2  = x^2 + √[2020 - x ]

 

0  =  √[ [2020 - x ]

 

x = 2020

 

cool cool cool

 Dec 20, 2019

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