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

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

Aromātai

$$4$$

Ngā Upane Otinga

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

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

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}.

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

Pūrua \sqrt{5}. Pūrua 2.

$$\frac{\sqrt{5}+2}{5-4}-\frac{1}{\sqrt{5}+2}$$

Tangohia te 4 i te 5, ka 1.

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

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

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

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

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

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}.

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

Pūrua \sqrt{5}. Pūrua 2.

$$\sqrt{5}+2-\frac{\sqrt{5}-2}{5-4}$$

Tangohia te 4 i te 5, ka 1.

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

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

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

Hei kimi i te tauaro o \sqrt{5}-2, kimihia te tauaro o ia taurangi.

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

Ko te tauaro o -2 ko 2.

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

Pahekotia te \sqrt{5} me -\sqrt{5}, ka 0.

$$2+2$$

Tāpirihia te 2 ki te 2, ka 4.

$$4$$

Tauwehe

$$2^{2}$$