Whakaoti i te 2/3u_k^2-60u_{13}+8662/3=0

$$\frac { 2 } { 3 } u _ { k } ^ { 2 } - 60 u _ { 13 } + 866 \frac { 2 } { 3 } = 0$$

Whakaoti mō u_13

$$u_{13}=\frac{u_{k}^{2}+1300}{90}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 3.

$$2u_{k}^{2}-180u_{13}+866\times 3+2=0$$

Whakareatia te 866 ki te 3, ka 2598.

$$2u_{k}^{2}-180u_{13}+2598+2=0$$

Tāpirihia te 2598 ki te 2, ka 2600.

$$2u_{k}^{2}-180u_{13}+2600=0$$

Tangohia te 2u_{k}^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-180u_{13}+2600=-2u_{k}^{2}$$

Tangohia te 2600 mai i ngā taha e rua.

$$-180u_{13}=-2u_{k}^{2}-2600$$

Whakawehea ngā taha e rua ki te -180.

$$\frac{-180u_{13}}{-180}=\frac{-2u_{k}^{2}-2600}{-180}$$

Mā te whakawehe ki te -180 ka wetekia te whakareanga ki te -180.

$$u_{13}=\frac{-2u_{k}^{2}-2600}{-180}$$

Whakawehe -2u_{k}^{2}-2600 ki te -180.

$$u_{13}=\frac{u_{k}^{2}}{90}+\frac{130}{9}$$

Whakaoti mō u_k (complex solution)

$$u_{k}=-\sqrt{90u_{13}-1300}$$

$$u_{k}=\sqrt{90u_{13}-1300}$$

Whakaoti mō u_k

$$u_{k}=\sqrt{90u_{13}-1300}$$

$$u_{k}=-\sqrt{90u_{13}-1300}\text{, }u_{13}\geq \frac{130}{9}$$