Question

$(\sqrt[6]{x} )^2-3\sqrt[6]{x} =4$

Answer 1

${( \sqrt[6]{x} )}^{2} - 3 \sqrt[6]{x} = 4 \\ \sqrt[6]{x} = y \\ {y}^{2} - 3y - 4 = 0 \\ d = 9 + 16 = 25 \\ y = \frac{3 + 5}{2} = 4 \\ y = \frac{3 - 5}{2} = - 1 \\ \\ \sqrt[6]{x} = 4 \: \: and \: \: \sqrt[6]{x} = - 1 \\ x = 4096 \: and \: \: x\in\varnothing \:$