Question

Tính giá trị biểu thức :

           \(M=\left(\frac{1}{4}\right)^{-\frac{3}{2}}-2\left(\frac{125}{27}\right)^{-\frac{2}{3}}+2^{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2-\sqrt{3}}}\)

Answer 1

Ta có:

\(\left(\frac{1}{4}\right)^{-\frac{3}{2}}=8\) ;

\(2\left(\frac{125}{27}\right)^{-\frac{2}{3}}=2.\frac{9}{25}=\frac{18}{25}\) ;

\(\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2-\sqrt{3}}=2\Rightarrow2^{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2-\sqrt{3}}}=2^2=4\)

\(\Rightarrow M=8-\frac{18}{25}+4=4\frac{18}{25}\)

Answer 2

Ta có \(\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2-\sqrt{3}}=\left(\sqrt{3}+1\right)\sqrt{4-2\sqrt{3}}=\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)=2\)

Nên \(B=2^{2\left(-\frac{3}{2}\right)}-2\left(\frac{5}{3}\right)^{3\left(-\frac{2}{3}\right)}+2^2=2^3-2\left(\frac{3}{5}\right)^2+4=\frac{282}{25}\)