3^x+3^(3-x)-12=0 решить уравнение

[latex] 3^{x} + 3^{3-x} -12=0, 3^{x} + \frac{ 3^{3} }{ 3^{x} } -12=0, \frac{1}{ 3^{x} } =t, 3^{x}= \frac{1}{t} , \frac{1}{t}+27t-12=0, 27 t^{2} -12t+1=0, t_{1}= \frac{6+ \sqrt{36-27} }{27} = \frac{6+3}{27} = \frac{1}{3} , t_{2} = \frac{6- \sqrt{36-27} }{27} = \frac{6-3}{27}= \frac{1}{9} , \frac{1}{ 3^{x} }= \frac{1}{3} , \frac{1}{ 3^{x} }= \frac{1}{ 3^{2} } x=1, x=2[/latex]