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Question Number 174291 by akolade last updated on 29/Jul/22

$$\mathrm{Find}$$$$\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}}$$$$\mathrm{if}\log \left(\frac{\mathrm{x}+\mathrm{y}}{3}\right)=\frac{\mathrm{logx}+\mathrm{logy}}{2}$$

Answered by Rasheed.Sindhi last updated on 29/Jul/22

$$\log \left(\frac{\mathrm{x}+\mathrm{y}}{3}\right)=\frac{\mathrm{logx}+\mathrm{logy}}{2};\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}}=?$$$$\log \left(\frac{\mathrm{x}+\mathrm{y}}{3}\right)=\frac{\mathrm{logxy}}{2}=\log \left({\left(\mathrm{xy}\right)}^{1/2}\right)$$$$\frac{\mathrm{x}+\mathrm{y}}{3}=\sqrt{\mathrm{xy}}$$$${\left(\frac{\mathrm{x}+\mathrm{y}}{3}\right)}^2=\mathrm{xy}$$$${\mathrm{x}}^2+2\mathrm{xy}+{\mathrm{y}}^2=9\mathrm{xy}$$$${\mathrm{x}}^2+{\mathrm{y}}^2=7xy$$$$\frac{{\mathrm{x}}^2+{\mathrm{y}}^2}{\mathrm{xy}}=7$$$$\frac{x}{y}+\frac{y}{x}=7$$

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