Whakaoti i te n/3+n=frac{sqrt{3}}{8}

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

Whakaoti mō n

$$n=\frac{24\sqrt{3}+9}{61}\approx 0.829003596$$

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. Me whakarea ngā taha e rua o te whārite ki te 8\left(n+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 3+n,8.

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

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

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

Tangohia te n\sqrt{3} mai i ngā taha e rua.

$$8n-n\sqrt{3}=3\sqrt{3}$$

Whakaraupapatia anō ngā kīanga tau.

$$-\sqrt{3}n+8n=3\sqrt{3}$$

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

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te -\sqrt{3}+8.

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

Mā te whakawehe ki te -\sqrt{3}+8 ka wetekia te whakareanga ki te -\sqrt{3}+8.

$$n=\frac{3\sqrt{3}}{8-\sqrt{3}}$$

Whakawehe 3\sqrt{3} ki te -\sqrt{3}+8.

$$n=\frac{24\sqrt{3}+9}{61}$$