MathDB

3

Part of 1965 Swedish Mathematical Competition

Problems(1)

for every x >= 1/2 exists n such that |x - n^2| <= \sqrt{x\frac{1}{4}}.

Source: 1965 Swedish Mathematical Competition p3

3/21/2021
Show that for every real x≥12x \ge \frac12 there is an integer nn such that ∣x−n2∣≤x−14|x - n^2| \le \sqrt{x-\frac{1}{4}}.
algebrainequalities