Find-x-y-y-x-if-log-x-y-3-logx-logy-2-

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

Find

\frac{x}{y} + \frac{y}{x}

if \log (\frac{x + y}{3}) = \frac{logx + logy}{2}

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

\log (\frac{x + y}{3}) = \frac{logx + logy}{2}; \frac{x}{y} + \frac{y}{x} = ?

\log (\frac{x + y}{3}) = \frac{logxy}{2} = \log ({(xy)}^{1 / 2})

\frac{x + y}{3} = \sqrt{xy}

{(\frac{x + y}{3})}^{2} = xy

x^{2} + 2 xy + y^{2} = 9 xy

x^{2} + y^{2} = 7 x y

\frac{x^{2} + y^{2}}{xy} = 7

\frac{x}{y} + \frac{y}{x} = 7