Question

Задания во вкладках.........

Answer 1

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

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