9. Calculează:
[tex]a)\:\sqrt{120}:\sqrt{30}-(\frac{1}{\sqrt2})^{-2}=\sqrt4-\sqrt{2}^2=2-2=\bf\red{\boxed{0}}\\[/tex]
[tex]b)\:(\frac{3}{\sqrt2})^{-2}\times(\frac{\sqrt6}{8}-\frac{1}{\sqrt6})=(\frac{\sqrt2}{3})^2\times(\frac{\sqrt6}{8}-\frac{\sqrt6}{6})=\frac{2}{9}\times(-\frac{\sqrt{6}}{24})=\bf-\frac{\sqrt6}{108}\\[/tex]
[tex]c)\:(3+\sqrt{12}):(\frac{1}{\sqrt3})^{-2}=(3+2\sqrt3):\sqrt3^2=(3+2\sqrt3):3=\bf\frac{3+2\sqrt3}{3}\\[/tex]
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Formulele ce le-am folosit pentru rezolvarea exercițiului:
[tex]\bf\red{\boxed{(\frac{1}{a})^{-n}=a^n}}[/tex]
[tex]\bf\blue{\boxed{(\frac{a}{b})^{-n}=(\frac{b}{a})^{n} }}[/tex]
Succes! ❀
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