X^4-29x^2+100=0 решить уравнение

Question

X^4-29x^2+100=0 решить уравнение

Comments

х^2=t; t^2-29t+100=0; t1+t2= 29; t1*t2= -100; t1= 20; t2= 4; x1= 400; x2= 16

Answer 1

x^4-29x^2+100=0
Пусть t = x^2
t^2 - 29t + 100 = 0
D = 841 - 400 = 441 = 21^2
t1 = (29 + 21)/2 = 25
t2 = (29-21)/2 = 4

t1 = 25 = x^2 => x1 = 5  x2 = -5
t2 = 4 = x^2 => x3 = 2 x4 = -2
Ответ: -5;-2;2;5