98/MR00. zadatak / Matematika - Zbirka rešenih zadataka

MR-98. zadatak

Racionalisati imenioc razlomka:

$\frac{1}{\sqrt{2} - \sqrt{7}} + \frac{1}{\sqrt{2} + \sqrt{7}}$

$\frac{1}{\sqrt{2} - \sqrt{7}} + \frac{1}{\sqrt{2} + \sqrt{7}}$

$= \frac{\sqrt{2} + \sqrt{7} + \sqrt{2} - \sqrt{7}}{(\sqrt{2} - \sqrt{7}) (\sqrt{2} + \sqrt{7})}$

$= \frac{2 \sqrt{2}}{{(\sqrt{2})}^{2} - {(\sqrt{7})}^{2}}$

$= \frac{2 \sqrt{2}}{2 - 7}$

$= - \frac{2 \sqrt{2}}{5}$

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