Solution:
we have been asked to find the solution of the equation
[tex]x^6 + 6x^3 + 5 = 0[/tex]
It can be solved using factoring as below:
[tex]x^6 + 6x^3 + 5 = 0\\\\substitute, x^3=y\\\\y^2+6y+5=0\\\\y^2+5y+y+5=0\\\\y(y+5)+1(y+5)=0\\\\(y+5)(y+1)=0\\\\y=-1,-5\\\\\text{substitute back }y=x^3\\\\x^3=-1,-5\\\\x=-1,\sqrt[3]{-5} \\\\\text{These are the only real solutions}\\[/tex]
