Question

Determine a solução da equação abaixo:

5x²15x+10=0

Answer 1

Resposta:

$5x^2\cdot \:15x+10=0\\\\\mathrm{Subtrair\:}10\mathrm{\:de\:ambos\:os\:lados}\\\\5x^2\cdot \:15x+10-10=0-10\\\\\mathrm{Simplificar}\\\\5x^2\cdot \:15x=-10\\\\Simplificar\\\\75x^3=-10\\\\\mathrm{Dividir\:ambos\:os\:lados\:por\:}75\\\\\frac{75x^3}{75}=\frac{-10}{75}\\\\\mathrm{Para\:}x^3=f\left(a\right)\mathrm{\:as\:solucoes\:sao\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}$

$x=\sqrt[3]{-\frac{2}{15}}\\\\\:x=\sqrt[3]{-\frac{2}{15}}\frac{-1+\sqrt{3}i}{2}\\\\\:x=\sqrt[3]{-\frac{2}{15}}\frac{-1-\sqrt{3}i}{2}\\\\x=-\sqrt[3]{\frac{2}{15}}\\\\\:x=\frac{15^{\frac{2}{3}}\sqrt[3]{2}}{30}-i\frac{5^{\frac{2}{3}}\sqrt[3]{2}\sqrt[6]{3}}{10}\\\\\:x=\frac{15^{\frac{2}{3}}\sqrt[3]{2}}{30}+i\frac{5^{\frac{2}{3}}\sqrt[3]{2}\sqrt[6]{3}}{10}$