((2+can3) (can (52-30can3))/2 -(2+can3) (can(26-15can3)

Giải thích các bước giải : \(\begin{array}{l} \frac{{(2 + \sqrt 3 )\sqrt {52 - 30\sqrt 3 } }}{2} - \left( {2 + \sqrt 3 } \right)\sqrt {26 - 15\sqrt 3 } \\ = \frac{{2 + \sqrt 3 }}{2}.\sqrt {52 - 30\sqrt 3 } - \frac{{2 + \sqrt 3 }}{{\sqrt 2 }}.\sqrt {52 - 30\sqrt 3 } \\ = \sqrt {52 - 30\sqrt 3 } \left( {\frac{{2 + \sqrt 3 }}{2} - \frac{{2\sqrt 2 + \sqrt 6 }}{2}} \right)\\ = \sqrt {52 - 30\sqrt 3 } .\frac{{2 - 2\sqrt 2 - \sqrt 6 + \sqrt 3 }}{2}\\ = \sqrt {25 - 2.15.\sqrt 3 + 27} .\,\frac{{2(1 - \sqrt 2 ) + \sqrt 3 (1 - \sqrt 2 )}}{2}\\ = \sqrt {25 - 2\sqrt {25} \sqrt {27} + 27} \,\,.\,\,\frac{{(2 + \sqrt 3 )(1 - \sqrt 2 )}}{2}\\ = \sqrt {{{\left( {5 - 3\sqrt 3 } \right)}^2}} \,\,.\,\,\frac{{(2 + \sqrt 3 )(1 - \sqrt 2 )}}{2} = \frac{{\left( {5 - 3\sqrt 3 } \right)\left( {2 + \sqrt 3 } \right)\left( {1 - \sqrt 2 } \right)}}{2} \end{array}\)