IMO Shortlist 1969 problem 65


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Dodao/la: arhiva
2. travnja 2012.
1969 alg identitet korijen shortlist
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(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