Em mong là đề bài đúng ._.
Phương trình có một nghiệm duy nhất
$x = \sqrt[3]{(\dfrac{(-b)^3}{27a^3}+\dfrac{bc}{6a^2}-\dfrac{d}{2a})+ \sqrt{(\dfrac{(-b)^3}{27a^3}+\dfrac{bc}{6a^2}-\dfrac{d}{2a})^2+ ( \dfrac{c}{3a}- \dfrac{b^2}{9a^2})^3}}+ \sqrt[3]{(\dfrac{(-b)^3}{27a^3}+\dfrac{bc}{6a^2}-\dfrac{d}{2a})- \sqrt{(\dfrac{(-b)^3}{27a^3}+\dfrac{bc}{6a^2}-\dfrac{d}{2a})^2+ ( \dfrac{c}{3a}- \dfrac{b^2}{9a^2})^3}} - \dfrac{b}{3a}$
$ = \sqrt[3]{(\dfrac{4^3}{27}+\dfrac{-16}{6}-1)+ \sqrt{(\dfrac{4^3}{27}+\dfrac{-16}{6}-1)^2+ ( \dfrac{4}{3}- \dfrac{16}{9})^3}}+ \sqrt[3]{(\dfrac{4^3}{27}+\dfrac{-16}{6}-1)- \sqrt{(\dfrac{4^3}{27}+\dfrac{-16}{6}-1)^2+ ( \dfrac{4}{3}- \dfrac{16}{9})^3}} - \dfrac{-4}{3}$
$ = \sqrt[3]{-\dfrac{35}{27} + \sqrt{\dfrac{1225}{729} - \dfrac{64}{729}}}\ + \sqrt[3]{-\dfrac{35}{27} - \sqrt{\dfrac{1225}{729} - \dfrac{64}{729}}} \ + \dfrac{4}{3}$
$ = \sqrt[3]{-\dfrac{35}{27} + \sqrt{\dfrac{43}{27}}} + \sqrt[3]{-\dfrac{35}{27} - \sqrt{\dfrac{43}{27}}} + \dfrac{4}{3}$
Bấm máy tính thì nghiệm xấp xỉ là $ -0,359304086$
