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min sum x^2/(ay + bz)(az + by)

Source: Switzerland - 2004 Swiss MO Final Round p5

December 26, 2022
algebrainequalities

Problem Statement

Let aa and bb be fixed positive numbers. Find the smallest possible depending on aa and bb value of the sum x2(ay+bz)(az+by)+y2(az+bx)(ax+bz)+z2(ax+by)(ay+bx),\frac{x^2}{(ay + bz)(az + by)}+\frac{y^2}{(az + bx)(ax + bz)}+\frac{z^2}{(ax + by)(ay + bx)}, where x,y,zx, y, z are positive real numbers.
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