IMO Shortlist 1969 problem 65

$(USS 2)$ Prove that for $a > b^2$ , the identity $\sqrt{a-b\sqrt{a+b\sqrt{a-b\sqrt{a+\cdots}}}}=\sqrt{a-\frac{3}{4}b^2}-\frac{1}{2}b$ holds.

Izvor: Međunarodna matematička olimpijada, shortlist 1969

Školjka