Whakaoti i te frac{2+sqrt{3}}{2-sqrt{3}}

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

Aromātai

$$4\sqrt{3}+7\approx 13.92820323$$

Ngā Upane Otinga

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

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

Whakaarohia te \left(2-\sqrt{3}\right)\left(2+\sqrt{3}\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}.

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

Pūrua 2. Pūrua \sqrt{3}.

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

Tangohia te 3 i te 4, ka 1.

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

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

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

Whakareatia te 2+\sqrt{3} ki te 2+\sqrt{3}, ka \left(2+\sqrt{3}\right)^{2}.

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2+\sqrt{3}\right)^{2}.

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

Ko te pūrua o \sqrt{3} ko 3.

$$4+4\sqrt{3}+3$$

Tāpirihia te 4 ki te 3, ka 7.

$$7+4\sqrt{3}$$