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Question Number 151142 by mathdanisur last updated on 18/Aug/21

if x; y; z \in R^{+} and \frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}} = \frac{27}{4}

prove that :

\frac{x^{3} + y^{2}}{x^{2} + y^{2}} + \frac{y^{3} + z^{2}}{y^{2} + z^{2}} + \frac{z^{3} + x^{2}}{z^{2} + x^{2}} ⩾ \frac{5}{2}