Chứng minh:

a) \(\left( {\sqrt {2025}  - \sqrt {2024} } \right)\left( {\sqrt {2025}  + \sqrt {2024} } \right) = 1\)

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

c) \({\left( {\sqrt 3  - 2} \right)^2}{\left( {\sqrt 3  + 2} \right)^2} = 1\)

a) \(VT = \left( {\sqrt {2025}  - \sqrt {2024} } \right)\left( {\sqrt {2025}  + \sqrt {2024} } \right)\)

\(\begin{array}{l} = {\left( {\sqrt {2025} } \right)^2} - {\left( {\sqrt {2024} } \right)^2}\\ = 2025 - 2024\end{array}\)

\( = 1 = VP.\)(đpcm)

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

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

\( = 3 - 1 = 2 = VP\) (đpcm).

c) \(VT = {\left( {\sqrt 3  - 2} \right)^2}{\left( {\sqrt 3  + 2} \right)^2}\)

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

\( = {\left( {3 - 4} \right)^2} = {\left( { - 1} \right)^2} = 1 = VP\) (đpcm).