Whakaoti i te frac{1+sqrt{5}}{sqrt{5}-2}

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

Aromātai

$$3\sqrt{5}+7\approx 13.708203932$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{1+\sqrt{5}}{\sqrt{5}-2} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}+2.

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

Whakaarohia te \left(\sqrt{5}-2\right)\left(\sqrt{5}+2\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}.

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

Pūrua \sqrt{5}. Pūrua 2.

$$\frac{\left(1+\sqrt{5}\right)\left(\sqrt{5}+2\right)}{5-4}$$

Tangohia te 4 i te 5, ka 1.

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

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 1+\sqrt{5} ki ia tau o \sqrt{5}+2.

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

Ko te pūrua o \sqrt{5} ko 5.

$$\sqrt{5}+2+5+2\sqrt{5}$$

Tāpirihia te 2 ki te 5, ka 7.

$$\sqrt{5}+7+2\sqrt{5}$$

Pahekotia te \sqrt{5} me 2\sqrt{5}, ka 3\sqrt{5}.

$$3\sqrt{5}+7$$