Question

3^x+3^(3-x)-12=0 решить уравнение

Answer 1

$3^{x} + 3^{3-x} -12=0, 3^{x} + frac{ 3^{3} }{ 3^{x} } -12=0, frac{1}{ 3^{x} } =t, 3^{x}= frac{1}{t} , frac{1}{t}+27t-12=0, 27 t^{2} -12t+1=0, t_{1}= frac{6+ sqrt{36-27} }{27} = frac{6+3}{27} = frac{1}{3} , t_{2} = frac{6- sqrt{36-27} }{27} = frac{6-3}{27}= frac{1}{9} , frac{1}{ 3^{x} }= frac{1}{3} , frac{1}{ 3^{x} }= frac{1}{ 3^{2} } x=1, x=2$