Question

rút gọn các biểu thức sau

a)\(A=\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}\) 

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

Answer 1

a: \(A^3=20+14\sqrt{2}+20-14\sqrt{2}+3\cdot\sqrt[3]{\left(20+14\sqrt{2}\right)\left(20-14\sqrt{2}\right)}\cdot A\)

\(\Leftrightarrow A^3=40+3\cdot2\cdot A=6A+40\)

\(\Leftrightarrow A^3-6A-40=0\)

=>A=4

b: \(B^3=182+\sqrt{33125}+182-\sqrt{33125}+3\cdot\sqrt[3]{\left(182+\sqrt{33125}\right)\left(182-\sqrt{33125}\right)}\cdot B\)

\(\Leftrightarrow B^3=364+3\cdot B\cdot\left(-1\right)=-3B+364\)

=>B=7