Question 1149213
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<pre>

You are given


    {{{sqrt(y + sqrt(y + sqrt(y + sqrt(y + ellipsis))))}}} = 5.          (1)


Square both sides.  Then the very first square root sign goes away, and you get


    y + {{{sqrt(y + sqrt(y + sqrt(y + sqrt(y + ellipsis))))}}}  = 25.    (2)


In the left side, the second addend is equal to 5, again (!)


So, your equation  (2)  takes the form


    y + 5 = 25.     (3).


From (3), you momentarily get


    y = 25 - 5 = 20.


<U>ANSWER</U>.  y = 20.
</pre>

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<pre>
    It is not a joke.  It is the standard way to solve such problems.


    <U>CHECK</U>.  Consider this sequence

            {{{sqrt(20)}}} = 4.472...

            {{{sqrt(20+sqrt(20))}}} = 4.947...

            {{{sqrt(20 + sqrt(20 + sqrt(20)))}}} = 4.995...


You see the sequence, which, OBVIOUSLY, converges, and converges to the value of 5.
</pre>


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