Question Number 136344 by Gideon last updated on 21/Mar/21
Commented by mindispower last updated on 21/Mar/21
$${x}^{\mathrm{2}} +\mathrm{6}{x}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{9} \\ $$$${t}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$$$\frac{\mathrm{5}}{\:\sqrt{{t}−\mathrm{1}}}+\frac{\mathrm{1}}{\:\sqrt{{t}−\mathrm{4}}}=\frac{\mathrm{4}}{{t}} \\ $$$${we}\:{have}\:{t}>\mathrm{4},{t}−\mathrm{1}>\mathrm{3}\Rightarrow\sqrt{{t}−\mathrm{1}}<{t}\Leftrightarrow \\ $$$$\frac{\mathrm{5}}{\:\sqrt{{t}−\mathrm{1}}}>\frac{\mathrm{4}}{\:\sqrt{{t}−\mathrm{1}}}>\frac{\mathrm{4}}{{t}}\: \\ $$$${no}\:{solution}\:{over}\:\mathbb{R} \\ $$$$ \\ $$