Question

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

Answer 1

$(\sqrt[6]{x} )^2-3\sqrt[6]{x} =4\\\\\sqrt[6]{x}=m,m\geq 0\\\\m^{2}-3m-4=0\\\\D=(-3)^{2}-4*(-4)=9+16=25=5^{2}\\\\m_{1}=\frac{3+5}{2}=4\\\\m_{2}=\frac{3-5}{2}=-1<0$

корень m₂ - не подходит, так как < 0

$\sqrt[6]{x}=4\\\\(\sqrt[6]{x})^{6}=4^{6}\\\\x=4096$