Question

prove that x/y+y/x=ksquare-2

Answer 1

$heya \\ \\ \\ \\ 2 log((x + y) \div k) = log(xy) \\ \\ \\ \\ \\ 2 log(x + y) - 2 log(k) = log(xy) \\ \\ \\ log((x + y) {}^{2} \div xy) = log(k {}^{2} ) \\ \\ \\( x + y) {}^{2} = k {}^{2} xy \\ \\ \\ x {}^{2} + y {}^{2} + 2xy = k {}^{2} xy \\ \\ \\ \\ x {}^{2} + y {}^{2} = xy(k {}^{2} - 2) \\ \\ \\ \\ divide \: both \: sides \: by \: xy \\ \\ \\ (x \div y) + (y \div x) = k {}^{2} - 2$