(x+3)^4-13 (x+3)^2+36=0

Question

(x+3)^4-13 (x+3)^2+36=0

Answer 1

(x+3)^2=y, y>=0
y^2-13y+36=0
D=169-144=25=5^2
y1=(13+5)/2=9
y2=8/2=4
(x+3)^2=9
(x+3)^2-3^2=0
(x+3-3)(x+3+3)=0
x(x+6)=0
x1=0
x2=-6
(x+3)^2=4
(x+3)^2-2^2=0
(x+3-2)(x+3+2)=0
(x+1)(x+5)=0
x3=-1
x4=-5
Ответ: x1=0; x2=-6; x3=-1; x4=-5