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if b^3+b <= a-a^3 for a,b>0 then b<a<1 and a^2+b^2<1

Source: Greece JBMO TST 2004 p4

June 18, 2019
algebrainequalities

Problem Statement

Let a,ba,b be positive real numbers such that b3+b≤a−a3b^3+b\le a-a^3. Prove that: i) b<a<1b<a<1 ii) a2+b2<1a^2+b^2<1
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