d..³√3+3-³√9
e.³√3+3-³√9
Jawaban:
9. A
10. A
Penjelasan dengan langkah-langkah:
9.
[tex] \frac{3}{ \sqrt[3]{5} - \sqrt[3]{2} } \\ = \frac{3( \sqrt[3]{5} {}^{2} + \sqrt[3]{5} \sqrt[3]{2} + \sqrt[3]{2} {}^{2} )}{ (\sqrt[3]{5} - \sqrt[3]{2} )( \sqrt[3]{5} {}^{2} + \sqrt[3]{5} \sqrt[3]{2} + \sqrt[3]{2} { }^{2} )} \\ = \frac{3( \sqrt[3]{5} {}^{2} + \sqrt[3]{10} + \sqrt[3]{2} {}^{2} )}{5 - 2} \\ = \sqrt[3]{5} {}^{2} + \sqrt[3]{10} + \sqrt[3]{2} {}^{2} \\ = {5}^{ \frac{2}{3} } + {10}^{ \frac{1}{3} } + {2}^{ \frac{2}{3} } [/tex]
10.
[tex] \frac{12}{ \sqrt[3]{9} + \sqrt[3]{3} } \\ = \frac{12( \sqrt[3]{9} {}^{2} - \sqrt[3]{9} \sqrt[3]{3} + \sqrt[3]{3} {}^{2} )}{( \sqrt[3]{9} + \sqrt[3]{3})(\sqrt[3]{9} {}^{2} - \sqrt[3]{9} \sqrt[3]{3} + \sqrt[3]{3} {}^{2}) } \\ = \frac{12(\sqrt[3]{9} {}^{2} - \sqrt[3]{9} \sqrt[3]{3} + \sqrt[3]{3} {}^{2})}{9 + 3} \\ = \frac{12(\sqrt[3]{9} {}^{2} - \sqrt[3]{9} \sqrt[3]{3} + \sqrt[3]{3} {}^{2})}{12} \\ = \sqrt[3]{9} {}^{2} - \sqrt[3]{27} + \sqrt[3]{3} {}^{2} \\ = \sqrt[3]{81} - 3 + \sqrt[3]{9} \\ = 3 \sqrt[3]{3} - 3 + \sqrt[3]{9} [/tex]
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