Задания во вкладках.........

$\sqrt{x-2} = \frac{x}{3} \\\ \left \{ {{3 \sqrt{x-2}=x } \atop {x \geq 2}} \right. \\\ \left \{ {{9(x-2)}=x ^2} \atop {x \geq 2}} \right. \\\ \left \{ {{x ^2-9x+18=0} \atop {x \geq 2}} \right. \\\ \left \{ {{D=9^2-4\cdot18=9} \atop {x \geq 2}} \right. \\\ \left \{ {{x_1= \frac{9+3}{2}=6; \ x_2= \frac{9-3}{2}=1} \atop {x \geq 2}} \right.$
Ответ: 6

$\sqrt[3]{x} + \sqrt[6]{x} -2=0 \ (y \geq 0) \\\ y^2+y-2=0 \\\ y^2+2y-y-2=0 \\\ y(y+2)-(y+2)=0 \\\ (y+2)(y-1)=0 \\\ y_1 \neq -2<0 \\\ y_2=1; \ \sqrt[6]{x} =1; \ x=1^6=1$
Ответ: 1

$\sqrt{x} -3 \sqrt[6]{x} -18=0 \ (x \geq 0) \\\ y^3-3y-18=0 \\\ y^3-3y^2+3y^2-9y+6y-18=0 \\\ y^2(y-3)+3y(y-3)+6(y-3)=0 \\\ (y-3)(y^2+3y+6)=0 \\\ y^2+3y+6=0 \\\ D=3^2-4\cdot6<0 \\\ y-3=0; \ y=3; \ \sqrt[6]{x} =3; \ x=3^6=729$
Ответ: 729