Question Number 122203 by help last updated on 14/Nov/20
Commented by Dwaipayan Shikari last updated on 14/Nov/20
$${K}^{\mathrm{2}} {x}+\mathrm{8}{y}=\mathrm{30} \\ $$$${Kx}+\mathrm{8}{y}=\mathrm{10} \\ $$$${x}\left({K}^{\mathrm{2}} −{K}\right)=\mathrm{20}\Rightarrow{K}^{\mathrm{2}} =\frac{\mathrm{20}}{{x}}+{K} \\ $$$${K}=\frac{\mathrm{1}+\sqrt{\mathrm{1}+\frac{\mathrm{80}}{{x}}}}{\mathrm{2}} \\ $$$${x}=\mathrm{1}\:\:{K}=\mathrm{5}\left(\:{Not}\:{satisfies}\right) \\ $$$${x}=\mathrm{10}\:\:\:{K}=\mathrm{2}\:\:\:\:\left({Satisfies}\right) \\ $$$${So}\:{K}^{\mathrm{2}} =\mathrm{4} \\ $$