Whakaoti i te 7/3+sqrt{2}+7/3-sqrt{2}=

$$\frac{ 7 }{ 3+ \sqrt{ 2 } } + \frac{ 7 }{ 3- \sqrt{ 2 } } =$$

Aromātai

$$6$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{7}{3+\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 3-\sqrt{2}.

$$\frac{7\left(3-\sqrt{2}\right)}{\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)}+\frac{7}{3-\sqrt{2}}$$

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

$$\frac{7\left(3-\sqrt{2}\right)}{3^{2}-\left(\sqrt{2}\right)^{2}}+\frac{7}{3-\sqrt{2}}$$

Pūrua 3. Pūrua \sqrt{2}.

$$\frac{7\left(3-\sqrt{2}\right)}{9-2}+\frac{7}{3-\sqrt{2}}$$

Tangohia te 2 i te 9, ka 7.

$$\frac{7\left(3-\sqrt{2}\right)}{7}+\frac{7}{3-\sqrt{2}}$$

Me whakakore te 7 me te 7.

$$3-\sqrt{2}+\frac{7}{3-\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{7}{3-\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 3+\sqrt{2}.

$$3-\sqrt{2}+\frac{7\left(3+\sqrt{2}\right)}{\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)}$$

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

$$3-\sqrt{2}+\frac{7\left(3+\sqrt{2}\right)}{3^{2}-\left(\sqrt{2}\right)^{2}}$$

Pūrua 3. Pūrua \sqrt{2}.

$$3-\sqrt{2}+\frac{7\left(3+\sqrt{2}\right)}{9-2}$$

Tangohia te 2 i te 9, ka 7.

$$3-\sqrt{2}+\frac{7\left(3+\sqrt{2}\right)}{7}$$

Me whakakore te 7 me te 7.

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

Tāpirihia te 3 ki te 3, ka 6.

$$6-\sqrt{2}+\sqrt{2}$$

Pahekotia te -\sqrt{2} me \sqrt{2}, ka 0.

$$6$$

Tauwehe

$$2\times 3$$