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system of inequalities

Source: LIMIT 2019 CBS1 P12

April 28, 2021
inequalities

Problem Statement

The system of inequalities a−b2≥14a-b^2\ge\frac14b−c2≥14b-c^2\ge\frac14c−d2≥14c-d^2\ge\frac14d−a2≥14d-a^2\ge\frac14where a,b,c,da,b,c,d are real numbers has <spanclass=′latex−bold′>(A)</span> no solutions<span class='latex-bold'>(A)</span>~\text{no solutions} <spanclass=′latex−bold′>(B)</span> exactly one solution<span class='latex-bold'>(B)</span>~\text{exactly one solution} <spanclass=′latex−bold′>(C)</span> exactly two solutions<span class='latex-bold'>(C)</span>~\text{exactly two solutions} <spanclass=′latex−bold′>(D)</span> infinitely many solutions<span class='latex-bold'>(D)</span>~\text{infinitely many solutions}
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