Whakaoti i te 2/sqrt{7+5}

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

Aromātai

$$\frac{5-\sqrt{7}}{9}\approx 0.261583188$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{2}{\sqrt{7}+5} mā te whakarea i te taurunga me te tauraro ki te \sqrt{7}-5.

$$\frac{2\left(\sqrt{7}-5\right)}{\left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right)}$$

Whakaarohia te \left(\sqrt{7}+5\right)\left(\sqrt{7}-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}.

$$\frac{2\left(\sqrt{7}-5\right)}{\left(\sqrt{7}\right)^{2}-5^{2}}$$

Pūrua \sqrt{7}. Pūrua 5.

$$\frac{2\left(\sqrt{7}-5\right)}{7-25}$$

Tangohia te 25 i te 7, ka -18.

$$\frac{2\left(\sqrt{7}-5\right)}{-18}$$

Whakawehea te 2\left(\sqrt{7}-5\right) ki te -18, kia riro ko -\frac{1}{9}\left(\sqrt{7}-5\right).

$$-\frac{1}{9}\left(\sqrt{7}-5\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{9} ki te \sqrt{7}-5.

$$-\frac{1}{9}\sqrt{7}-\frac{1}{9}\left(-5\right)$$

Tuhia te -\frac{1}{9}\left(-5\right) hei hautanga kotahi.

$$-\frac{1}{9}\sqrt{7}+\frac{-\left(-5\right)}{9}$$

Whakareatia te -1 ki te -5, ka 5.

$$-\frac{1}{9}\sqrt{7}+\frac{5}{9}$$