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IMO LongList 1967, Hungary 5

Source: IMO LongList 1967, Hungary 5

December 16, 2004
algebravectorInequalitygeometric inequality3D geometryIMO ShortlistIMO Longlist

Problem Statement

Prove that for an arbitrary pair of vectors ff and gg in the space the inequality af2+bfg+cg2≥0af^2 + bfg +cg^2 \geq 0 holds if and only if the following conditions are fulfilled: a \geq 0,   c \geq 0,   4ac \geq b^2.
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