Question

Розвʼязати рівняння за дискримінантом

Answer 1

$\displaystyle\bf\\3\cdot 9^{x} +2\cdot\cdot 3^{x} -1=0\\\\3\cdot(3^{x})^{2} +2\cdot 3^{x} -1=0\\\\3^{x} =m \ , \ m > 0\\\\3m^{2} +2m-1=0\\\\D=2^{2} -4\cdot (-1)\cdot 3=4+12-100=16=4^{2} \\\\\\m_{1} =\frac{-2+4}{6}=\frac{2}{6} =\frac{1}{3} \\\\\\m_{2} =\frac{-2-4}{6} =\frac{-6}{6} =-1 < 0 \ ne \ podxodit\\\\m=\frac{1}{3} \\\\3^{x} =\frac{1}{3} \\\\3^{x} =3^{-1} \\\\\boxed{x=-1}\\\\Otvet \ : \ -1$