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

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

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  1. Giải thích các bước giải :

    \(\begin{array}{l}
    \frac{{(2 + \sqrt 3 )\sqrt {52 – 30\sqrt 3 } }}{2} – \left( {2 + \sqrt 3 } \right)\sqrt {26 – 15\sqrt 3 } \\
    = \frac{{2 + \sqrt 3 }}{2}.\sqrt {52 – 30\sqrt 3 } – \frac{{2 + \sqrt 3 }}{{\sqrt 2 }}.\sqrt {52 – 30\sqrt 3 } \\
    = \sqrt {52 – 30\sqrt 3 } \left( {\frac{{2 + \sqrt 3 }}{2} – \frac{{2\sqrt 2 + \sqrt 6 }}{2}} \right)\\
    = \sqrt {52 – 30\sqrt 3 } .\frac{{2 – 2\sqrt 2 – \sqrt 6 + \sqrt 3 }}{2}\\
    = \sqrt {25 – 2.15.\sqrt 3 + 27} .\,\frac{{2(1 – \sqrt 2 ) + \sqrt 3 (1 – \sqrt 2 )}}{2}\\
    = \sqrt {25 – 2\sqrt {25} \sqrt {27} + 27} \,\,.\,\,\frac{{(2 + \sqrt 3 )(1 – \sqrt 2 )}}{2}\\
    = \sqrt {{{\left( {5 – 3\sqrt 3 } \right)}^2}} \,\,.\,\,\frac{{(2 + \sqrt 3 )(1 – \sqrt 2 )}}{2} = \frac{{\left( {5 – 3\sqrt 3 } \right)\left( {2 + \sqrt 3 } \right)\left( {1 – \sqrt 2 } \right)}}{2}
    \end{array}\)

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