Question

Решите уравнение, используя введение новой переменной:
(x^2-10x)^2-3(x^2-10)-4=0

Answer 1

(x²-10x)²-3(x²-10x)-4=0
t=x²-10x
t²-3t-4=0
t(1)=-1(корни найдены по т.Виета)
t(2)=4
x²-10x=-1                                       x²-10x=4
x²-10x+1=0                                    x²-10x-4=0
D=96                                             D=116
x1=(10+4√6)/2=5+2√6                  x3=(10-2√29)/2=5-√29
x2=5-2√6                                      x4=5+√29