Question

cho x = \(\dfrac{\sqrt[3]{10+6\sqrt{3}}.\left(\sqrt{3}-1\right)}{\sqrt{6+2\sqrt{5}}-\sqrt{5}}\)

tính p=(x³-4x+1)²⁰¹⁵

Answer 1

Ta có :

\(x=\dfrac{\sqrt[3]{10+6\sqrt{3}}\left(\sqrt{3}-1\right)}{\sqrt{6+2\sqrt{5}}-\sqrt{5}}\)

\(\Leftrightarrow x=\dfrac{\sqrt[3]{3\sqrt{3}+9+3\sqrt{3}+1}\left(\sqrt{3}-1\right)}{\sqrt{5+2\sqrt{5}+1}-\sqrt{5}}\)

\(\Leftrightarrow x=\dfrac{\sqrt[3]{\left(\sqrt{3}+1\right)^3}\left(\sqrt{3}-1\right)}{\sqrt{\left(\sqrt{5}+1\right)^2-5}}\)

\(\Leftrightarrow x=\dfrac{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}{\sqrt{5}+1-\sqrt{5}}\)

\(\Leftrightarrow x=\dfrac{3-1}{1}=2\)

thay x=2 vào biểu thức P ta có :

\(P=\left(2^3-4.2+1\right)^{2015}\)

\(P=1^{2015}=1\)

Nhớ like đúng cho mk nha mọi người