Tìm n ∈ Z (n+5) ² = 64(n-2) ³

` (n + 5)^2 = 64(n – 2)^3 `

` => (n + 5)^2 = 4^{3}(n – 2)^3 `

` => (n + 5)^2 = [4(n – 2)]^{3} `

` => (n + 5)^2 = (4n – 8)^{3} `

` => n^2 + 2n.5 + 5^2 = 4n^3 + 3.4n^{2}.8 + 3.4n.8^{2} – 8^{2} `

` => n^2 + 10n + 25 – 4n^3 + 96n^{2} + 768n – 64 = 0 `

` => -4n^{3} + n^{2} + 96n^{2} + 10n + 768n + 25 – 64 = 0 `

` => -4n^3 + 97n^2 + 778n – 39 = 0 `

` => n = 3 `