What are all the solutions to the equation \(x^5 = x^3\)?

x 5 = x 3 x 5 − x 3 = 0 x 3 ( x 2 − 1 ) = 0 x 3 = 0 x 2 − 1 = 0 x = 0 Δ = b 2 − 4 a c = − 4 ∗ 1 ∗ ( − 1 ) = 4 Δ ​ = 4 ​ = 2 x 1 ​ = 2 a − b − Δ ​ ​ = 2 0 − 2 ​ = − 1 x 2 ​ = 2 a − b + Δ ​ ​ = 2 0 + 2 ​ = 1 x ∈ { − 1 ; 0 ; 1 }

Answered by Yipes | 2024-06-10

x 5 = x 3 x 5 − x 3 = 0 x 3 ( x 2 − 1 ) = 0 x 3 ( x − 1 ) ( x + 1 ) = 0 x = 0 ∨ x = 1 ∨ x = − 1

Answered by konrad509 | 2024-06-10

The solutions to the equation x 5 = x 3 are x = − 1 , 0 , and 1 . We found these solutions by factoring the equation into two separate parts. Thus, all solutions combined yield a set of three values: { − 1 , 0 , 1 } .
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Answered by Yipes | 2024-12-26