แก้โจทย์ {l}{5x^3-6x+8=0}{y=0}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { 5 x ^ {3} - 6 x + 8 = 0 }\\ { y = 0 }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

หาค่า x, y, z, a, b, c (complex solution)

$$x=\frac{\sqrt[3]{2}\times 25^{\frac{2}{3}}\left(\sqrt[3]{3\sqrt{10}-10}+\sqrt[3]{-3\sqrt{10}-10}\right)}{25}\approx 0.752244078+1.302924962i\text{, }y=0\text{, }z=0\text{, }a=0\text{, }b=0\text{, }c=0$$

$$x=-\frac{\sqrt[3]{2}\times 25^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{3\sqrt{10}-10}i-\sqrt[3]{3\sqrt{10}-10}+2\sqrt[3]{-3\sqrt{10}-10}\right)}{100}\approx 0.234787196-1.004171092i\text{, }y=0\text{, }z=0\text{, }a=0\text{, }b=0\text{, }c=0$$

$$x=-\frac{\sqrt[3]{2}\times 25^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{3\sqrt{10}-10}+2\sqrt[3]{-3\sqrt{10}-10}+\sqrt{3}\sqrt[3]{3\sqrt{10}-10}i\right)}{100}\approx -0.987031274-0.29875387i\text{, }y=0\text{, }z=0\text{, }a=0\text{, }b=0\text{, }c=0$$

หาค่า x, y, z, a, b, c

$$c=0$$