find the real roots of
An important idea when solving questions with infinite nested radicals.
If
Then we can rewrite the equation as
As it is as infinite succession, we are allowed to 'cut' the expression anywhere convenient and let it be equal to the L.H.S.
Example (from Pi in the Sky: Issue 11)
. Find
Answer
With this technique, you could solve your question now, I'll give another example then move on to your question.
In general, if
Then
And
Now to your question
Then using our technique, we convert to
The real roots are and .
Don't hesitate to ask anymore questions.
God bless your mathematical endeavours.