Nested Square Roots

Algebra Level 5

If 4+44+4=a+bc\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-\cdots}}}}=\frac{a+\sqrt{b}}{c} such that the fraction in the RHS cannot be simplified any further and bb is square free and a,b,ca,b,c are all integers, what is the value of a+b+ca + b + c?

Extra Credit: Post a solution that can do it by hand without the requirement of quartic formula.

×

Problem Loading...

Note Loading...

Set Loading...