Question

[Nguyễn Bá Minh]

Với \(x=-\frac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}+\sqrt{2}}\) Tính giá trị của  :\(f\left(x\right)=1+x^2+x^3+x^4+....+x^{2016}\)

Answer 1

[Phan Văn Hiếu]

\(x=-\frac{2\sqrt{3+\sqrt{5-\sqrt{12+2\sqrt{12}+1}}}}{\sqrt{6}+\sqrt{2}}\)

\(x=-\frac{2\sqrt{3+\sqrt{5-\sqrt{\left(\sqrt{12}+1\right)^2}}}}{\sqrt{6}+\sqrt{2}}\)

\(x=-\frac{2\sqrt{3+\sqrt{5-\sqrt{12}-1}}}{\sqrt{6}+\sqrt{2}}\)

\(x=-\frac{2\sqrt{3+\sqrt{4-2\sqrt{3}}}}{\sqrt{6}+\sqrt{2}}\)

\(x=-\frac{2\sqrt{3+\sqrt{3-2\sqrt{3}+1}}}{\sqrt{6}+\sqrt{2}}\)

\(x=-\frac{2\sqrt{3+\sqrt{\left(\sqrt{3}-1\right)^2}}}{\sqrt{6}+\sqrt{2}}\)

\(x=-\frac{2\sqrt{3+\sqrt{3}-1}}{\sqrt{6}+\sqrt{2}}\)

\(x=-\frac{2\sqrt{2+\sqrt{3}}}{\sqrt{2}\left(\sqrt{3}+1\right)}\)

\(x=-\frac{\sqrt{2}\sqrt{2+\sqrt{3}}}{\left(\sqrt{3}+1\right)}\)

\(x=-\frac{\sqrt{4+2\sqrt{3}}}{\sqrt{3}+1}\)

\(x=-\frac{\sqrt{3+2\sqrt{3}+1}}{\sqrt{3}+1}\)

\(x=-\frac{\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{3}+1}\)

\(x=-\frac{\sqrt{3}+1}{\sqrt{3}+1}=-1\)

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