Question

Chứng minh rằng:

a) \(\left(1-\sqrt{2}\right)^2=3-2\sqrt{2}\);                           b) \(\left(\sqrt{3}+\sqrt{2}\right)^2=5+2\sqrt{6}\).

Answer 1

a) \({\left( {1 - \sqrt 2 } \right)^2}\)\( = {1^2} - 2.1.\sqrt 2  + {\left( {\sqrt 2 } \right)^2}\)\( = 1 - 2\sqrt 2  + 2\)\( = 3 - 2\sqrt 2 ;\)

b) \({\left( {\sqrt 3  + \sqrt 2 } \right)^2}\)\( = {\sqrt 3 ^2} + 2.\sqrt 3 .\sqrt 2  + {\left( {\sqrt 2 } \right)^2}\)\( = 3 + 2\sqrt 6  + 2\)\( = 5 + 2\sqrt 6 \)