Revers al inegalitatii H. - F. intr-un triunghi particular

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Mateescu Constantin
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Revers al inegalitatii H. - F. intr-un triunghi particular

Post by Mateescu Constantin »

Aratati ca intr-un triunghi \( ABC \) ale carui unghiuri satisfac o relatie de tipul \( A\ge B\ge 60^{\circ}\ge C \)

are loc inegalitatea : \( \fbox{\ a^2\ +\ b^2\ +\ c^2\ \le\ 4S\sqrt 3\ +\ \frac 43\ \cdot\ \[(a-b)^2\ +\ (b-c)^2\ +\ (c-a)^2\]\ } \) .
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