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Inequality Iran 2015

Source: Iranian third round - Algebra exam 2015 (problem1)

September 8, 2015
inequalities

Problem Statement

x,y,zx,y,z are three real numbers inequal to zero satisfying x+y+z=xyzx+y+z=xyz. Prove that ∑(x2−1x)2≥4 \sum (\frac{x^2-1}{x})^2 \geq 4
Proposed by Amin Fathpour
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