Whakaoti i te n/3+n=sqrt{3div8}

$$\frac{ n }{ 3+n } = \sqrt{ 3 \div 8 }$$

Whakaoti mō n

$$n = \frac{6 \sqrt{6} + 9}{5} \approx 4.739387691$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe n ki -3 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te n+3.

$$n=\left(n+3\right)\sqrt{\frac{3}{8}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{3}{8}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{3}}{\sqrt{8}}.

$$n=\left(n+3\right)\times \frac{\sqrt{3}}{\sqrt{8}}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$n=\left(n+3\right)\times \frac{\sqrt{3}}{2\sqrt{2}}$$

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

$$n=\left(n+3\right)\times \frac{\sqrt{3}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$n=\left(n+3\right)\times \frac{\sqrt{3}\sqrt{2}}{2\times 2}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$n=\left(n+3\right)\times \frac{\sqrt{6}}{2\times 2}$$

Whakareatia te 2 ki te 2, ka 4.

$$n=\left(n+3\right)\times \frac{\sqrt{6}}{4}$$

Tuhia te \left(n+3\right)\times \frac{\sqrt{6}}{4} hei hautanga kotahi.

$$n=\frac{\left(n+3\right)\sqrt{6}}{4}$$

Whakamahia te āhuatanga tohatoha hei whakarea te n+3 ki te \sqrt{6}.

$$n=\frac{n\sqrt{6}+3\sqrt{6}}{4}$$

Tangohia te \frac{n\sqrt{6}+3\sqrt{6}}{4} mai i ngā taha e rua.

$$n-\frac{n\sqrt{6}+3\sqrt{6}}{4}=0$$

Whakareatia ngā taha e rua o te whārite ki te 4.

$$4n-\left(n\sqrt{6}+3\sqrt{6}\right)=0$$

Hei kimi i te tauaro o n\sqrt{6}+3\sqrt{6}, kimihia te tauaro o ia taurangi.

$$4n-n\sqrt{6}-3\sqrt{6}=0$$

Me tāpiri te 3\sqrt{6} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$4n-n\sqrt{6}=3\sqrt{6}$$

Pahekotia ngā kīanga tau katoa e whai ana i te n.

$$\left(4-\sqrt{6}\right)n=3\sqrt{6}$$

Whakawehea ngā taha e rua ki te 4-\sqrt{6}.

$$\frac{\left(4-\sqrt{6}\right)n}{4-\sqrt{6}}=\frac{3\sqrt{6}}{4-\sqrt{6}}$$

Mā te whakawehe ki te 4-\sqrt{6} ka wetekia te whakareanga ki te 4-\sqrt{6}.

$$n=\frac{3\sqrt{6}}{4-\sqrt{6}}$$

Whakawehe 3\sqrt{6} ki te 4-\sqrt{6}.

$$n=\frac{6\sqrt{6}+9}{5}$$