Question

найдите x^3+3x^2+2=0​

Answer 1

$x^3+3x^2+2=0\\x=y-\frac{b}{3a}\\p=-\frac{b^2}{3a^2}+\frac{c}{a}=-3\\q=\frac{2b}{27a^3}-\frac{bc}{3a^2}+\frac{d}{a}=\frac{20}{9}\\y=\sqrt[3]{-\frac{q}{2}+\sqrt{\frac{q^2}{4}+\frac{p^3}{27}}}+\sqrt[3]{-\frac{q}{2}-\sqrt{\frac{q^2}{4}+\frac{p^3}{27}}}\\y=\sqrt[3]{-\frac{10}{9}+\sqrt{\frac{100}{81}-1}}+\sqrt[3]{-\frac{10}{9}-\sqrt{\frac{100}{81}-1}}\\x=\sqrt[3]{-\frac{10}{9}+\sqrt{\frac{19}{81}}}+\sqrt[3]{-\frac{10}{9}-\sqrt{\frac{19}{81}}}-1$