Whakaoti i te 6sqrt{2m-n}=5t

$$6 \sqrt { 2 m - n } = 5 t$$

Whakaoti mō m

$$m=\frac{25t^{2}}{72}+\frac{n}{2}$$

$$t\geq 0$$

Ngā Upane mō te Whakaoti Whārite Pūtake

Whakawehea ngā taha e rua ki te 6.

$$\frac{6\sqrt{2m-n}}{6}=\frac{5t}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$\sqrt{2m-n}=\frac{5t}{6}$$

Pūruatia ngā taha e rua o te whārite.

$$2m-n=\frac{25t^{2}}{36}$$

Me tango -n mai i ngā taha e rua o te whārite.

$$2m-n-\left(-n\right)=\frac{25t^{2}}{36}-\left(-n\right)$$

Mā te tango i te -n i a ia ake anō ka toe ko te 0.

$$2m=\frac{25t^{2}}{36}-\left(-n\right)$$

Tango -n mai i \frac{25t^{2}}{36}.

$$2m=\frac{25t^{2}}{36}+n$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2m}{2}=\frac{\frac{25t^{2}}{36}+n}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$m=\frac{\frac{25t^{2}}{36}+n}{2}$$

Whakawehe \frac{25t^{2}}{36}+n ki te 2.

$$m=\frac{25t^{2}}{72}+\frac{n}{2}$$

Whakaoti mō n

$$n=-\frac{25t^{2}}{36}+2m$$

$$t\geq 0$$

Ngā Upane mō te Whakaoti Whārite Pūtake

Whakawehea ngā taha e rua ki te 6.

$$\frac{6\sqrt{-n+2m}}{6}=\frac{5t}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$\sqrt{-n+2m}=\frac{5t}{6}$$

Pūruatia ngā taha e rua o te whārite.

$$-n+2m=\frac{25t^{2}}{36}$$

Me tango 2m mai i ngā taha e rua o te whārite.

$$-n+2m-2m=\frac{25t^{2}}{36}-2m$$

Mā te tango i te 2m i a ia ake anō ka toe ko te 0.

$$-n=\frac{25t^{2}}{36}-2m$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-n}{-1}=\frac{\frac{25t^{2}}{36}-2m}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$n=\frac{\frac{25t^{2}}{36}-2m}{-1}$$

Whakawehe \frac{25t^{2}}{36}-2m ki te -1.

$$n=-\frac{25t^{2}}{36}+2m$$

Whakaoti mō m (complex solution)

$$m=\frac{25t^{2}}{72}+\frac{n}{2}$$

$$arg(t)<\pi \text{ or }t=0$$

Whakaoti mō n (complex solution)

$$n=-\frac{25t^{2}}{36}+2m$$

$$arg(t)<\pi \text{ or }t=0$$