Whakaoti i te 4/sqrt{2-6}

$$\frac{ 4 }{ \sqrt{ 2 } -6 }$$

Aromātai

$$\frac{-2\sqrt{2}-12}{17}\approx -0.872260419$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{4}{\sqrt{2}-6} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}+6.

$$\frac{4\left(\sqrt{2}+6\right)}{\left(\sqrt{2}-6\right)\left(\sqrt{2}+6\right)}$$

Whakaarohia te \left(\sqrt{2}-6\right)\left(\sqrt{2}+6\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}.

$$\frac{4\left(\sqrt{2}+6\right)}{\left(\sqrt{2}\right)^{2}-6^{2}}$$

Pūrua \sqrt{2}. Pūrua 6.

$$\frac{4\left(\sqrt{2}+6\right)}{2-36}$$

Tangohia te 36 i te 2, ka -34.

$$\frac{4\left(\sqrt{2}+6\right)}{-34}$$

Whakawehea te 4\left(\sqrt{2}+6\right) ki te -34, kia riro ko -\frac{2}{17}\left(\sqrt{2}+6\right).

$$-\frac{2}{17}\left(\sqrt{2}+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{2}{17} ki te \sqrt{2}+6.

$$-\frac{2}{17}\sqrt{2}-\frac{2}{17}\times 6$$

Tuhia te -\frac{2}{17}\times 6 hei hautanga kotahi.

$$-\frac{2}{17}\sqrt{2}+\frac{-2\times 6}{17}$$

Whakareatia te -2 ki te 6, ka -12.

$$-\frac{2}{17}\sqrt{2}+\frac{-12}{17}$$

Ka taea te hautanga \frac{-12}{17} te tuhi anō ko -\frac{12}{17} mā te tango i te tohu tōraro.

$$-\frac{2}{17}\sqrt{2}-\frac{12}{17}$$