Question

Tính P\(=\left(x^3+12x-9\right)^{2021}\) khi \(x=\sqrt[3]{4\left(\sqrt{5}+1\right)}-\sqrt[3]{4\left(\sqrt{5}-1\right)}\)

Answer 1

`x=\root{3}{4(\sqrt5+1)}-\root{3}{4(\sqrt5-1)}`

`<=>x^3=4(sqrt5+1)-4(\sqrt5-1)-3\root{3}{16(5-1)}(\root{3}{4(\sqrt5+1)}-\root{3}{4(\sqrt5-1)})`

`<=>x^3=4\sqrt5+4-4sqrt5+4-3\root{3}{64}x`

`<=>x^3=8-12x`

`<=>x^3+12x-8=0`

`=>P=(x^3+12-8-1)^2021=(-1)^2021=-1`

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