Question

rút gon biểu thức 

E=\(\sqrt[3]{182+\sqrt{33125}}+\sqrt[3]{182-\sqrt{33125}}\)

Answer 1

\(E^3=182+\sqrt{33125}+182-\sqrt{33125}+3\sqrt[3]{182^2-33125}\left(E\right)\)

   =\(364-3E\)

\(\Rightarrow E^3+3E-364=0\) 

\(\Leftrightarrow E^3-7E^2+7E^2-49E+52E-364=0\)

\(\Leftrightarrow\left(E-7\right)\left(E^2+7E+52\right)=0\)

\(\Rightarrow E=7\)

Answer 2

ta có \(E^3=\left(\sqrt[3]{182+\sqrt{33125}}+\sqrt[3]{182-\sqrt{33125}}\right)^3\)

\(E^3=\left(182+\sqrt{33125}\right)+\left(182-\sqrt{33125}\right)+3\cdot E\cdot\sqrt[3]{33124-33125}\)

\(E^3=364-3E\)

giải phương trình \(E^3+3E-364=0\)

suy ra E= 7