Question

tính P=\(x^3+y^3-3\left(x+y\right)+2014\)

biết \(x=\sqrt[3]{3+2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\);\(y=\sqrt[3]{17+12\sqrt{2}}+\sqrt[3]{17-12\sqrt{2}}\)

Answer 1

Co :  X=\(\sqrt[3]{3-2\sqrt{2}}+\sqrt[3]{3+2\sqrt{2}}\)

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

\(\Leftrightarrow x^3=6+3x\)

CMTT : \(y^3=34+3y\)\(\)

\(\Leftrightarrow x^3+y^3-3\left(x+y\right)+2014=6+3x+34+3y-3x-3y+2014\)\(=2054\)