Question Number 169439 by Giantyusuf last updated on 30/Apr/22
Answered by mr W last updated on 30/Apr/22
$${a}^{\mathrm{2}} {x}^{\mathrm{2}} +{a}^{\mathrm{2}} {y}^{\mathrm{2}} +{b}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} {y}^{\mathrm{2}} =\mathrm{81}×\mathrm{121}\:\:\:…\left({i}\right) \\ $$$${a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{2}{abxy}=\mathrm{99}^{\mathrm{2}} \:\:\:…\left({ii}\right) \\ $$$$\left({i}\right)−\left({ii}\right): \\ $$$${a}^{\mathrm{2}} {y}^{\mathrm{2}} +{b}^{\mathrm{2}} {x}^{\mathrm{2}} −\mathrm{2}{abxy}=\mathrm{81}×\mathrm{121}−\mathrm{99}^{\mathrm{2}} =\mathrm{0} \\ $$$$\left({ay}−{bx}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$$\Rightarrow{ay}−{bx}=\mathrm{0} \\ $$