x^7 + 27x^4=0

Question

all real solutions

Answer 1

from:

1)  x^7 + 27x^4=0   we get

 

2)  x^4(x^3 + 27)=0

 

     we have:  x^3 + 27 =x^3 + 3^3 = (x+3)(x^2-3x+9), so:

 

3)  x^4(x+3)(x^2-3x+9)=0  which is equivalent to following three equations:

 

4)  x^4 = 0  ;  x+3 = 0  ;   x^2-3x+9 = 0  - the last one has no real solutions, hence we get:

 

5)  x1=0   x2=-3