Question Number 172007 by Mikenice last updated on 23/Jun/22
$${solve}: \\ $$$${x}\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:−{x}^{\mathrm{2}} =−\mathrm{6} \\ $$
Answered by puissant last updated on 23/Jun/22
$${x}\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:=\:{x}^{\mathrm{2}} −\mathrm{6} \\ $$$$\Rightarrow\:{x}^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{4}\right)={x}^{\mathrm{4}} −\mathrm{12}{x}^{\mathrm{2}} +\mathrm{36} \\ $$$$\Rightarrow\:{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} ={x}^{\mathrm{4}} −\mathrm{12}{x}^{\mathrm{2}} +\mathrm{36} \\ $$$$\Rightarrow\:\mathrm{16}{x}^{\mathrm{2}} −\mathrm{36}=\mathrm{0} \\ $$$$\Rightarrow\:\left(\mathrm{4}{x}\right)^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} =\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{4}{x}=\mathrm{6}\:\:{or}\:\:\:\mathrm{4}{x}=−\mathrm{6} \\ $$$$\Rightarrow\:{x}=\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:{or}\:\:\:{x}=−\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}=\left\{−\frac{\mathrm{2}}{\mathrm{3}}\:\:;\:\:\frac{\mathrm{2}}{\mathrm{3}}\:\right\} \\ $$
Commented by Mikenice last updated on 23/Jun/22
$${please}\:{sir}\:{recheck}\:{your}\:{solution} \\ $$