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Find the maximum value of x^3+2y

Source: 2021 Turkey JBMO TST P4

May 23, 2021
inequalities2-variable inequalityalgebraTurkey

Problem Statement

Let x,y,zx,y,z be real numbers such that ∣yz−xz∣≤1 and ∣yz+xz∣≤1\left|\dfrac yz-xz\right|\leq 1\text{ and }\left|yz+\dfrac xz\right|\leq 1 Find the maximum value of the expression x3+2yx^3+2y
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