Question

Помогите решить!!!! ​

Answer 1

Ответ:

Объяснение:

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

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

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

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

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