The \( \infty \)-radical madness 2
Algebra
Level
5
Let \[ A:=\sqrt{8-\sqrt{8-\sqrt{8+\sqrt{8-\sqrt{8-\sqrt{8+\cdots}}}}}} \] \[ B:=\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+\cdots}}}}} \] Find \( B-A \).
Details and assumptions:
The sign pattern in the first radical is \( (--+) \).
by
Max Filippov