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

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

Aromātai

$$\text{Indeterminate}$$

Ngā Upane Otinga

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

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

Whakaarohia te \left(\sqrt{-2}-1\right)\left(\sqrt{-2}+1\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}.

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

Pūrua \sqrt{-2}. Pūrua 1.

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

Tangohia te 1 i te -2, ka -3.

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

Whakareatia te \sqrt{-2}+1 ki te \sqrt{-2}+1, ka \left(\sqrt{-2}+1\right)^{2}.

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{-2}+1\right)^{2}.

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

Tātaihia te \sqrt{-2} mā te pū o 2, kia riro ko -2.

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

Tāpirihia te -2 ki te 1, ka -1.

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

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{1-2\sqrt{-2}}{3}$$

Aromātai (complex solution)

$$\frac{-2\sqrt{2}i+1}{3}\approx 0.333333333-0.942809042i$$

Wāhi Tūturu (complex solution)

$$\frac{1}{3} = 0.3333333333333333$$