Question

Tính giá trị của đa thức \(\left(x^{31}-5x^{10}+3\right)^{2018}\)

 tại x= 9-\(\dfrac{1}{\sqrt{\dfrac{9}{4}-\sqrt{5}}}+\dfrac{1}{\sqrt{\dfrac{9}{4}+\sqrt{5}}}\)

Answer 1

\(x=9-\dfrac{2}{\sqrt{9-4\sqrt{5}}}+\dfrac{2}{\sqrt{9+4\sqrt{5}}}=9-\dfrac{2}{\sqrt{\left(\sqrt{5}-2\right)^2}}+\dfrac{2}{\sqrt{\left(\sqrt{5}+2\right)^2}}\)

\(=9-\dfrac{2}{\sqrt{5}-2}+\dfrac{2}{\sqrt{5}+2}=9+\dfrac{2\left(\sqrt{5}-2-\sqrt{5}-2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}\)

\(=9+\left(-8\right)=1\)

\(\Rightarrow\left(1^{31}-5.1^{10}+3\right)^{2018}=\left(-1\right)^{2018}=1\)