Asosiy tarkibga o'tish

1.3-bo'lim : Radikallar

17. Ayiruvchini ratsionalizatsiya qiling. \(x\) ijobiy deb faraz qiling.

\[\frac{9}{{\sqrt[3]{{2x}}}}\]
Yechim

Bu masalani hal qilish uchun maxrajni ratsionalizatsiya qilish uchun pay va maxrajni \(\sqrt[3]{{{{\left( {2x} \right)}^2}}}\) ga ko'paytirishimiz kerak.

\[\frac{9}{{\sqrt[3]{{2x}}}} = \frac{9}{{\sqrt[3]{{2x}}}}\frac{{\sqrt[3]{{{{\left( {2x} \right)}^2}}}}}{{\sqrt[3]{{{{\left( {2x} \right)}^2}}}}} = \frac{{9\,\,\sqrt[3]{{{{\left( {2x} \right)}^2}}}}}{{\sqrt[3]{{{{\left( {2x} \right)}^3}}}}} = \frac{{9\,\,\sqrt[3]{{{{\left( {2x} \right)}^2}}}}}{{2x}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{9\,\,\sqrt[3]{{4{x^2}}}}}{{2x}}}}\]