Whakaoti i te 12/9+sqrt{7}

$$\frac { 12 } { 9 + \sqrt { 7 } }$$

Aromātai

$$\frac{54-6\sqrt{7}}{37}\approx 1.030418706$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{12}{9+\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te 9-\sqrt{7}.

$$\frac{12\left(9-\sqrt{7}\right)}{\left(9+\sqrt{7}\right)\left(9-\sqrt{7}\right)}$$

Whakaarohia te \left(9+\sqrt{7}\right)\left(9-\sqrt{7}\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}.

$$\frac{12\left(9-\sqrt{7}\right)}{9^{2}-\left(\sqrt{7}\right)^{2}}$$

Pūrua 9. Pūrua \sqrt{7}.

$$\frac{12\left(9-\sqrt{7}\right)}{81-7}$$

Tangohia te 7 i te 81, ka 74.

$$\frac{12\left(9-\sqrt{7}\right)}{74}$$

Whakawehea te 12\left(9-\sqrt{7}\right) ki te 74, kia riro ko \frac{6}{37}\left(9-\sqrt{7}\right).

$$\frac{6}{37}\left(9-\sqrt{7}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{6}{37} ki te 9-\sqrt{7}.

$$\frac{6}{37}\times 9+\frac{6}{37}\left(-1\right)\sqrt{7}$$

Tuhia te \frac{6}{37}\times 9 hei hautanga kotahi.

$$\frac{6\times 9}{37}+\frac{6}{37}\left(-1\right)\sqrt{7}$$

Whakareatia te 6 ki te 9, ka 54.

$$\frac{54}{37}+\frac{6}{37}\left(-1\right)\sqrt{7}$$

Whakareatia te \frac{6}{37} ki te -1, ka -\frac{6}{37}.

$$\frac{54}{37}-\frac{6}{37}\sqrt{7}$$