Whakaoti i te 2/3-sqrt{5}

$$\frac { 2 } { 3 - \sqrt { 5 } }$$

Aromātai

$$\frac{\sqrt{5}+3}{2}\approx 2.618033989$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{2}{3-\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te 3+\sqrt{5}.

$$\frac{2\left(3+\sqrt{5}\right)}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}$$

Whakaarohia te \left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(3+\sqrt{5}\right)}{3^{2}-\left(\sqrt{5}\right)^{2}}$$

Pūrua 3. Pūrua \sqrt{5}.

$$\frac{2\left(3+\sqrt{5}\right)}{9-5}$$

Tangohia te 5 i te 9, ka 4.

$$\frac{2\left(3+\sqrt{5}\right)}{4}$$

Whakawehea te 2\left(3+\sqrt{5}\right) ki te 4, kia riro ko \frac{1}{2}\left(3+\sqrt{5}\right).

$$\frac{1}{2}\left(3+\sqrt{5}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 3+\sqrt{5}.

$$\frac{1}{2}\times 3+\frac{1}{2}\sqrt{5}$$

Whakareatia te \frac{1}{2} ki te 3, ka \frac{3}{2}.

$$\frac{3}{2}+\frac{1}{2}\sqrt{5}$$