Question Number 220405 by MathematicalUser2357 last updated on 12/May/25
$$\mathrm{9}^{{x}^{\mathrm{2}} } −\mathrm{3}^{{x}+\mathrm{1}} =\mathrm{0} \\ $$
Answered by MathematicalUser2357 last updated on 12/May/25
$${x}=\mathrm{1} \\ $$
Answered by mr W last updated on 12/May/25
$$\mathrm{3}^{\mathrm{2}{x}^{\mathrm{2}} } =\mathrm{3}^{{x}+\mathrm{1}} \\ $$$$\Rightarrow\mathrm{2}{x}^{\mathrm{2}} ={x}+\mathrm{1} \\ $$$$\Rightarrow\mathrm{2}{x}^{\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\left(\mathrm{2}{x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow{x}=\mathrm{1},\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$