Question

Chứng minh:

a) \(\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)=1\);                    b) \(\left(\sqrt[3]{2}+1\right)\left[\left(\sqrt[3]{2}\right)^2-\sqrt[3]{2}+1\right]=3\).

Answer 1

a. Ta có:

\(\left( {2 - \sqrt[{}]{3}} \right)\left( {2 + \sqrt[{}]{3}} \right) = {2^2} - {\left( {\sqrt[{}]{3}} \right)^2} = 4 - 3 = 1\).

b. Ta có:

\(\left( {\sqrt[3]{2} + 1} \right)\left[ {{{\left( {\sqrt[3]{2}} \right)}^2} - \sqrt[3]{2} + 1} \right] = {\left( {\sqrt[3]{2}} \right)^3} + {1^3} = 2 + 1 = 3\).