Question

способом введениа новой переменной решите уравнения
х4-х2-6=0
(х-1)2-13(х-1)+36=0​

Answer 1

a)x⁴-x²-6 = 0

x² = t, t>=0

t²-t-6 = 0

По Виету:

{t1+t2 = 1

{t1•t2 = -6

t1 = 3

t2 = -2 < 0

x² = 3

x = ±√3

2)(x-1)²-13(x-1)+36 = 0

x-1 = a

a²-13a+36 = 0

По Виету:

{A1+A2 = 13

{a1•a2 = 36

A1 = 9

A2 = 4

x - 1 = 9

x = 10

x - 1 = 4

x = 5