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Find the range of c satisfying an inequality.

Source: 2018 China Southeast MO Grade 10 P1

July 30, 2018
algebraInequalityinequalities

Problem Statement

Assume cc is a real number. If there exists x∈[1,2]x\in[1,2] such that max⁡{∣x+cx∣,∣x+cx+2∣}≥5\max\left\{\left |x+\frac cx\right |, \left |x+\frac cx + 2\right |\right\}\geq 5, please find the value range of cc.
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