Answer:
let a = x² (a ≥ 0), we have the equation:
a² + a + 1 = 0
⇔ a² + 2.1/2.a + 1/4 + 3/4 = 0
⇔ (a + 1/2)² = -3/4 (unreasonable)
=> no solutions
Step-by-step explanation:
Answer:
(x2−x+1)(x2+x+1)
Step-by-step explanation:
Let’s multiply by x2−1
(x4+x2+1)(x2–1)=x6+x4+x2−x4−x2−1=x6−1
So x4+x2+1=x6−1x2−1 .
Now, let’s factorize x6−1 differently: x6−1=(x3+1)(x3−1) . Also x2−1=(x+1)(x−1) .
So x4+x2+1=(x3+1)(x3−1)(x+1)(x−1)=x3+1x+1⋅x3−1x−1 .
Now, I can factorize x3+1=(x+1)(x2−x+1) and x3−1=(x−1)(x2+x+1) .
So. x4+x2+1=(x2−x+1)(x2+x+1) .
