how to solve this equation ?

[abdlaziz]

this is first time to me in this amazing forum

can any body tell me how to solve this equation?

factor this equation :

x[sup]8[/sup]+x[sup]4[/sup]+1

[Math Tutor]

Could you write the equation, please?

[tex]x^8 + 2x^4 + 1 = x^8 + 2x^4 + 1 - x^4 =[/tex]
[tex]= (x^4 + 1)^2 - x^4 = (x^4 + 1 - x^2)(x^4 + 1 + x^2)=[/tex]
[tex]= (x^4 + 2x + 1 - 3x^2)(x^4 + 2x^2+1 - x^2)=[/tex]
[tex]= ((x^2 + 1)^2 - 3x^2)((x^2 +1)^2 - x^2)=[/tex]
[tex]= (x^2 + 1 - sqrt{3}x)(x^2 + 1 - sqrt{3}x)(x^2 +1 - x)(x^2 +1 + x)=[/tex]

May you continue, please?

[martosss]

[tex]= (x^4 + 1)^2 - x^4 = (x^4 + 1 - x^2)(x^4 + 1 + x^2)=[/tex]
[tex]= (x^4 + 2x + 1 - 3x^2)(x^4 + 2x^2+1 - x^2)=[/tex]

Your result is correct, but you have technical mistakes!
[tex](x^4+1-x^2)(x^4+1+x^2)=[/tex]
[tex]\left[(x^2-1)^2+x^2\right]\left[(x^2+\frac{1}{2})^2+\frac{3}{4}\right][/tex]
You can also present it as
[tex](x^4+\frac{1}{2})^2+\frac{3}{4}[/tex], which has no solutions if it is equal to 0.