Question

Rezolvare completa va rog frumos! Dau coronita! ​

Answer 1

$4\sqrt{24}(\frac{9}{\sqrt{18}} -  \frac{4}{\sqrt{12}}) - 5(\sqrt{27} - \sqrt{32})\\\\8\sqrt{6}(\frac{9\sqrt{18}}{18} - \frac{4\sqrt{12}}{12}) - 5(3\sqrt{3} - 4\sqrt{2})\\\\8\sqrt{6}(\frac{\sqrt{18}}{2} - \frac{\sqrt{12}}{3}) - 5(3\sqrt{3} - 4\sqrt{2}\\\\8\sqrt{6}(\frac{3\sqrt{2}}{2} - \frac{2\sqrt{3}}{3}) - 15\sqrt{3} + 20\sqrt{2}\\\\\[tex]\frac{24\sqrt{12}}{2} - \frac{16\sqrt{18}}{3} - 15\sqrt{3} + 20\sqrt{2}\\\\\\12\sqrt{12}-\frac{48\sqrt{2}}{3}-15\sqrt{3}+20\sqrt{2}\\\\24\sqrt{3}-\frac{48\sqrt{2}}{3}-15\sqrt{3}+\frac{60\sqrt2}{3}\\\\9\sqrt{3}+\frac{12\sqrt{2}}{3}\\\\9\sqrt{3}+4\sqrt{2}$[/tex]

Answer 2

$\displaystyle\bf\\~~~~4\sqrt{24}\left(\frac{9}{\sqrt{18}}-\frac{4}{\sqrt{12}}\right)-5\Big(\sqrt{27}-\sqrt{32}\Big)=\\\\\\=4\sqrt{4\times6}\left(\frac{9}{\sqrt{9\times2}}-\frac{4}{\sqrt{4\times3}}\right)-5\Big(\sqrt{9\times3}-\sqrt{16\times2}\Big)=\\\\\\=4\times2\sqrt{6}\left(\frac{9}{3\sqrt{2}}-\frac{4}{2\sqrt{3}}\right)-5\Big(3\sqrt{3}-4\sqrt{2}\Big)=\\\\\\=8\sqrt{6}\left(\frac{3}{\sqrt{2}}-\frac{2}{\sqrt{3}}\right)-\Big(15\sqrt{3}-20\sqrt{2}\Big)=$

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$\displaystyle\bf\\=\frac{24\sqrt{6}}{\sqrt{2}}-\frac{16\sqrt{6}}{\sqrt{3}}-15\sqrt{3}+20\sqrt{2}=\\\\\\=\frac{24\sqrt{3}\sqrt{2}}{\sqrt{2}}-\frac{16\sqrt{3}\sqrt{2}}{\sqrt{3}}-15\sqrt{3}+20\sqrt{2}=\\\\\\=\underline{24\sqrt{3}}-\underbrace{16\sqrt{2}}-\underline{15\sqrt{3}}+\underbrace{20\sqrt{2}}=\boxed{\bf9\sqrt{3}+4\sqrt{2}}$