Question

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Answer 1

Ответ:

Объяснение:

$\displaystyle \[\frac{{{{\left( {{{24}^{\frac{1}{4}}}+{6^{\frac{1}{4}}}}\right)}^2}}}{{4\cdot {3^{\frac{1}{2}}}+3\cdot {6^{\frac{1}{2}}}}}=\frac{{{{\left( {{{24}^{\frac{1}{4}}}} \right)}^2}+2 \cdot {{24}^{\frac{1}{4}}}\cdot {6^{\frac{1}{4}}}+{{\left( {{6^{\frac{1}{4}}}}\right)}^2}}}{{4 \cdot {3^{\frac{1}{2}}}+3 \cdot {2^{\frac{1}{2}}} \cdot {3^{\frac{1}{2}}}}}=\]$

$\displaystyle \[=\frac{{{{24}^{\frac{1}{2}}}+2 \cdot {{24}^{\frac{1}{4}}} \cdot {6^{\frac{1}{4}}}+{6^{\frac{1}{2}}}}}{{{3^{\frac{1}{2}}} \cdot \left({4+3\cdot {2^{\frac{1}{2}}}}\right)}}=\frac{{{{24}^{\frac{1}{2}}}+2\cdot {4^{\frac{1}{4}}}\cdot {6^{\frac{1}{4}}} \cdot {6^{\frac{1}{4}}}+{6^{\frac{1}{2}}}}}{{{3^{\frac{1}{2}}}\cdot \left( {4+3\cdot {2^{\frac{1}{2}}}}\right)}}=\]$

$\displaystyle \[=\frac{{{{24}^{\frac{1}{2}}}+2\cdot {4^{\frac{1}{4}}}\cdot {6^{\frac{1}{2}}}+{6^{\frac{1}{2}}}}}{{{3^{\frac{1}{2}}}\cdot \left( {4+3\cdot {2^{\frac{1}{2}}}}\right)}}=\frac{{{3^{\frac{1}{2}}}\cdot \left( {{8^{\frac{1}{2}}}+2\cdot {4^{\frac{1}{4}}} \cdot {2^{\frac{1}{2}}}+{2^{\frac{1}{2}}}}\right)}}{{{3^{\frac{1}{2}}}\cdot \left( {4+3\cdot {2^{\frac{1}{2}}}}\right)}}=\]$

$\displaystyle \[=\frac{{{8^{\frac{1}{2}}}+2\cdot {2^{\frac{1}{2}}}\cdot {2^{\frac{1}{2}}}+{2^{\frac{1}{2}}}}}{{4+3\cdot {2^{\frac{1}{2}}}}}=\frac{{{2^{\frac{1}{2}}}\cdot \left( {{4^{\frac{1}{2}}}+2\cdot {2^{\frac{1}{2}}}+1}\right)}}{{{2^{\frac{1}{2}}}\cdot \left( {2\cdot {2^{\frac{1}{2}}}+3}\right)}}=\]$

$\displaystyle \[=\frac{{2+2\cdot {2^{\frac{1}{2}}}+1}}{{2\cdot {2^{\frac{1}{2}}}+3}}=\frac{{2 \cdot {2^{\frac{1}{2}}}+3}}{{2\cdot {2^{\frac{1}{2}}}+3}}=\boxed 1\]$