Lovely equation

Post author By cbokhove
Post date January 13, 2012

On this weblog I encountered a great equation that can be solved in a creative way (the dots denote that the expression in repeated infinitely). I have reproduced it here:

(I) $\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}=4$

square both sides

(II) ${x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}=16$

now substitute I in II

$x+4=16$

gives

$x=12$

By cbokhove

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By cbokhove