Question

Tìm giá trị biểu thức:

\(\left(2x^5+2x^4-x^3+1\right)^{2013}+\frac{\left(2x^3+2x^2-x-3\right)^{2013}}{2x^4+2x^3-x^2-3^{2013}}\)

Với \(x=\sqrt{\frac{2-\sqrt{3}}{2}}\)

Answer 1

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

\(\Rightarrow2x=\sqrt{3}-1\Rightarrow2x+1=\sqrt{3}\Rightarrow\left(2x+1\right)^2=3\Leftrightarrow4x^2+4x+1=3\Leftrightarrow4x^2+4x-2=0\Leftrightarrow2x^2+2x-1=0\)

nên đề bài = \(\left(x^3\left(2x^2+2x-1\right)+1\right)^{2013}+\frac{\left(x\left(2x^2+2x-1\right)-3\right)^{2013}}{x^2\left(2x^2+2x-1\right)-3^{2013}}\)

 =\(\left(0+1\right)^{2013}+\frac{\left(0-3\right)^{2013}}{0-3^{2013}}=1+1=2\)