If \( a x^{2}+b / x \geq c \) for all positive \( x \) where \( a0 \) and \( b0 \), then show th...

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If \( a x^{2}+b / x \geq c \) for all positive \( x \) where \( a0 \) and \( b0 \), then show that \( 27 a b^{2} \geq 4 c^{3} \).
(1982, 2M)
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