Question

решите уравнение (x^2-3x)^2-(x^2-3x)-8=0

Answer 1

(x^2-3x)^2-(x^2-3x)-8=0

x^2-3x=t

t^2-t-8=0

D=1+4*8=33

t_1=(1+sqrt(33))/2

t_2=(1-sqrt(33))/2

x^2-3x-(1+sqrt(33))/2=0

D=9+2+2sqrt(33)=11+2sqrt(33)

x_12=(3+-sqrt(11+2sqrt(33))/2

x^2-3x+(sqrt(33)-1)/2=0

D=9-2sqrt(33)+2<0

Ответ: (3+-sqrt(11+2sqrt(33))/2