Ответ:

[tex] \sqrt[3]{x + 1} + 2 \sqrt[6]{x + 1} = 3 \\ \\ \sqrt[6]{x + 1} = y \\ x + 1 \geqslant 0 [/tex]

[tex] {y}^{2} + 2y = 3 \\ {y}^{2} + 2y - 3 = 0 \\ \\ y 1 + y2 = 2 \\ y1y2 = - 3 \\ \\ y1 = - 1 \\ y2 = 3[/tex]

[tex] \sqrt[6]{x1 + 1} = - 1 \\ x1 + 1 = 1 \\ x1 = 0[/tex]

[tex] \sqrt[6]{x2 + 1} = 3 \\ x2 + 1 = 729 \\ x2 = 728[/tex]

[tex] \sqrt[3]{x + 1} + 2 \sqrt[6]{x + 1} = 3 \\ \\ \sqrt[3]{1} + 2 \sqrt[6]{1} = 3 \: \: \: - \: \: \: correct \\ \sqrt[3]{729} + 2 \sqrt[6]{729 } = 3 \\ 9 + 6 = 3 \: \: \: - \: incorrect[/tex]

ответ: х = 0