x=∛(-b/2+√(b^2/4+a^3/27)) + ∛(-b/2-√(b^2/4+a^3/27))
Tính A= x^3+ax+b
ĐKXĐ: ...
[tex]x^{3}=\frac{-b}{2}+\sqrt{\frac{b^{2}}{2}+\frac{a^{3}}{27}}+\frac{-b}{2}-\sqrt{\frac{b^{2}}{2}+\frac{a^{3}}{27}}+[/tex] +[tex]3.\sqrt[3]{(\frac{-b}{2}+\sqrt{\frac{b^{2}}{2}+\frac{a^{3}}{27}}).(\frac{-b}{2}-\sqrt{\frac{b^{2}}{2}+\frac{a^{3}}{27}})}.[/tex] [tex]\left ( \sqrt[3]{\frac{-b}{2}+\sqrt{\frac{b^{2}}{4}+\frac{a^{3}}{27}}} +\sqrt[3]{\frac{-b}{2}-\sqrt{\frac{b^{2}}{4}+\frac{a^{3}}{27}}}\right )[/tex]
[tex]\Leftrightarrow x^{3}=-b+3.\sqrt[3]{\frac{b^{2}}{4}-\frac{b^{2}}{4}-\frac{a^{3}}{27}}[/tex].x
[tex]\Leftrightarrow x^{3}=-b-ax[/tex]
[tex]\Leftrightarrow x^{3}+ax+b=0[/tex]
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