←Vrati se na zadatke1. ZadatakRacionaliziraj razlomak 12+3−5\dfrac1{\sqrt2+\sqrt3-\sqrt5}2+3−51.Prikaži rješenjeRješenje12+3−5=12+3−5⋅2+3+52+3+5=2+3+5(2+3)2−5=2+3+526=2+3+526⋅66=6(2+3+5)12\begin{aligned} \frac1{\sqrt2+\sqrt3-\sqrt5}&=\frac1{\sqrt2+\sqrt3-\sqrt5}\cdot\frac{\sqrt2+\sqrt3+\sqrt5}{\sqrt2+\sqrt3+\sqrt5}\\ &=\frac{\sqrt2+\sqrt3+\sqrt5}{(\sqrt2+\sqrt3)^2-5}=\frac{\sqrt2+\sqrt3+\sqrt5}{2\sqrt6}\\ &=\frac{\sqrt2+\sqrt3+\sqrt5}{2\sqrt6}\cdot\frac{\sqrt6}{\sqrt6}\\ &=\frac{\sqrt6(\sqrt2+\sqrt3+\sqrt5)}{12} \end{aligned}2+3−51=2+3−51⋅2+3+52+3+5=(2+3)2−52+3+5=262+3+5=262+3+5⋅66=126(2+3+5)Pomakni formulu lijevo ili desno.
