How can I solve [tex]x^3 + 7x = 8x^2[/tex]?

x 3 + 7 x = 8 x 2 / − 8 x 2 x 3 − 8 x 2 + 7 x = 0 x ( x 2 − 8 x + 7 ) = 0 ⟺ x = 0 ∨ x 2 − 8 x + 7 = 0
x 2 − 8 x + 7 = 0 a = 1 ; b = − 8 ; c = 7 Δ = b 2 − 4 a c ; x 1 ​ = 2 a − b − Δ ​ ​ ; x 2 ​ = 2 a − b + Δ ​ ​ Δ = ( − 8 ) 2 − 4 ⋅ 1 ⋅ 7 = 64 − 28 = 36 ; Δ ​ = 36 ​ = 6 x 1 ​ = 2 ⋅ 1 8 − 6 ​ = 2 2 ​ = 1 ; x 2 ​ = 2 ⋅ 1 8 + 6 ​ = 2 14 ​ = 7 A n s w er : x = 0 or x = 1 or x = 7.

Answered by Anonymous | 2024-06-10

x 3 + 7 x = 8 x 2 x 3 − 8 x 2 + 7 x = 0 x ( x 2 − 8 x + 7 ) = 0 x = 0 ∨ x 2 − 8 x + 7 = 0 Δ = b 2 − 4 a c = ( − 8 ) 2 − 4 ∗ 1 ∗ 7 = 64 − 28 = 36
x 1 ​ = 2 a − b − Δ ​ ​ = 2 8 − 36 ​ ​ = 2 8 − 6 ​ = 2 2 ​ = 1 x 2 ​ = 2 a − b + Δ ​ ​ = 2 8 + 36 ​ ​ = 2 8 + 6 ​ = 2 14 ​ = 7 A n s w er : x = 0 ∨ x = 1 ∨ x = 7

Answered by Lilith | 2024-06-10

To solve the equation x 3 + 7 x = 8 x 2 , we rearrange it to x 3 − 8 x 2 + 7 x = 0 and factor it. This gives us the solutions x = 0 , x = 1 , and x = 7 .
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Answered by Anonymous | 2024-12-24