Question

 

giúp mình bài trong ảnh vưới ạ 

 

1.4. Tính \( T = \sqrt{2 + \sqrt{3} \cdot \sqrt{2 + \sqrt{2 + \sqrt{3} \cdot \sqrt{2 - \sqrt{2 + \sqrt{3}}}}}} \).

Answer 1

`T = \sqrt{2+\sqrt{3}} . \sqrt{2+\sqrt{2+\sqrt{3}}} . \sqrt{2 - \sqrt{2+\sqrt{3}}}`

`T = \sqrt{2+\sqrt{3}} . \sqrt{(2+\sqrt{2+\sqrt{3}})(2 - \sqrt{2} + \sqrt{3})}`

`T = \sqrt{2+\sqrt{3}} . \sqrt{4 - (2 + \sqrt{3})^2}`

`T = \sqrt{2+\sqrt{3}} . \sqrt{4 - |2 + \sqrt{3}|}`

`T = \sqrt{2 + \sqrt{3}} . \sqrt{4 - 2 - \sqrt{3}}`

`T = \sqrt{2 + \sqrt{3}} . \sqrt{2 - \sqrt{3}}`

`T = \sqrt{(2 + \sqrt{3})(2 - \sqrt{3})}`

`T = \sqrt{4 - 3}`

`T = \sqrt{1} = 1`