x3+2x2−4x+83=0x3+2x2-4x+83=0
⇔(x+(2⇔(x+(2 3√2+123+1)23)3=0)23)3=0
⇔x=−(2⇔x=-(23√223+1)23+1)23.
`x^3 + 2x^2 - 4x + 8/3 = 0`
`<=>` \(\left(x+\dfrac{2\left(\sqrt[3]{2}+1\right)^2}{3}\right)^3=0\)
`<=>`\(x=-\dfrac{2\left(\sqrt[3]{2}+1\right)^2}{3}^3\)
\(\Leftrightarrow3x^3+6x^2-12x+8=0\)
\(\Leftrightarrow4x^3-\left(x^3-6x^2+12x-8\right)=0\)
\(\Leftrightarrow4x^3-\left(x-2\right)^3=0\)
\(\Leftrightarrow\left(\sqrt[3]{4}x\right)^3=\left(x-2\right)^3\)
\(\Leftrightarrow\sqrt[3]{4}x=x-2\)
\(\Leftrightarrow x=\dfrac{-2}{\sqrt[3]{4}-1}\)
