Question

243x^2+81x-216=0
помогите решить

Answer 1

$243x^2+81x-216=0 |:9,\27x^2+9x-24=0 |:3,\9x^2+3x-8=0,\\D=3^2-4cdot9cdot(-8)=9+288=297,\\x_{1,2}=frac{-3pmsqrt{297}}{2cdot9}=frac{-3pmsqrt{11cdot27}}{18}=frac{-3pmsqrt{11cdot3cdot3^2}}{18}=frac{-3pm3sqrt{33}}{18}=frac{-1+sqrt{33}}{6};\\x_1=frac{-1+sqrt{33}}{6},\x_2=frac{-1-sqrt{33}}{6}.\\OTBET: x_1=frac{-1+sqrt{33}}{6}, x_2=frac{-1-sqrt{33}}{6}.$