Question

Giúp ạ.

Answer 1

Ta có: \(a=\sqrt[3]{2-\sqrt3}+\sqrt[3]{2+\sqrt3}\)

=>\(a^3=2-\sqrt3+2+\sqrt3+3\cdot\sqrt[3]{\left(2-\sqrt3\right)\left(2+\sqrt3\right)}\cdot a\)

=>\(a^3=4+3a\)

=>\(a^3-3a-4=0\)

=>\(a^3-a^2+a^2-a+4a-4=0\)

=>\(\left(a-1\right)\left(a^2+a+4\right)=0\)

=>a-1=0

=>a=1

\(M=\frac{64}{\left(a^2-3\right)^3}-3a=\frac{64}{\left(1-3\right)^3}-3\cdot1=\frac{64}{\left(-2\right)^3}-3=-8-3=-11\)

=>M không là số chính phương