Question 65
(USS 2) Prove that for $a>b^2$,
$$\sqrt{a-b\sqrt{a+b\sqrt{a-b\sqrt{a+\cdots}}}}=\sqrt{a-\frac34b^2}-\frac12b.$$
$$\sqrt{a-b\sqrt{a+b\sqrt{a-b\sqrt{a+\cdots}}}}=\sqrt{a-\frac34b^2}-\frac12b.$$
IMO 1969 - Longlist Problems Question 65
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