How do you solve x^{3}-1=0?

Gabriela Duarte

Gabriela Duarte

Answered question

2022-01-30

How do you solve x31=0?

Answer & Explanation

Dominique Green

Dominique Green

Beginner2022-01-31Added 11 answers

Step 1
We use (a3b3)=(ab)(a2+ab+b2)
Therefore
(x31)=(x1)(x2+x+1)=0
(x1)=0 and (x2+x+1)=0
x=1
For the equation, x2+x+1=0
We calculate the discriminant,
Δ=b24ac=14×1×1=3
As, Δ>0, we do not a solution in R but in C
x=1±Δ2=1±i32
x1=12+i32 and x2=12i32

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