This week, we learn about Vieta Root Jumping, a descent method which uses Vieta's formula to find additional solutions.
You should first read up on Vieta’s Formula.
How would you use Vieta Root Jumping to solve the following?
[IMO 2007/5] Let \(a\) and \(b\) be positive integers. Show that if \( 4ab-1 \mid (4a^2-1)^2 \), then \(a=b \).
Share a problem which uses the Vieta root jumping technique.