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Question Number 195404 by universe last updated on 01/Aug/23

Answered by deleteduser1 last updated on 01/Aug/23

$$(\frac{{127}^2}{xy}+\frac{x}{y}+\frac{y}{x})(127+x+y)$$$$=\frac{{127}^3}{xy}+\frac{{127}^2}{y}+\frac{{127}^2}{x}+\frac{127x}{y}+\frac{x^2}{y}+x+\frac{127y}{x}+y+\frac{y^2}{x}$$$$=(\frac{{127}^3}{xy}+x+y)+\frac{{127}^2}{y}+\frac{y^2}{x}+\frac{127x}{y}+\frac{{127}^2}{x}+\frac{x^2}{y}+\frac{127y}{x}$$$$⩾3\sqrt[3]{{127}^3}+6\sqrt[6]{{127}^6}=9\left(127\right)=1143$$$$(Equalityholdswhenx=y=127)$$

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