Whakaoti i te y=5pi^3/17-sqrt{2x}

$$y = \frac { 5 \pi ^ { 3 } } { 17 } - \sqrt { 2 x }$$

Whakaoti mō x

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

$$y\leq \frac{5\pi ^{3}}{17}$$

Ngā Upane mō te Whakaoti Whārite Pūtake

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{5\pi ^{3}}{17}-\sqrt{2x}=y$$

Tangohia te \frac{5\pi ^{3}}{17} mai i ngā taha e rua.

$$-\sqrt{2x}=y-\frac{5\pi ^{3}}{17}$$

Whakareatia ngā taha e rua o te whārite ki te 17.

$$-17\sqrt{2x}=17y-5\pi ^{3}$$

Whakawehea ngā taha e rua ki te -17.

$$\frac{-17\sqrt{2x}}{-17}=\frac{17y-5\pi ^{3}}{-17}$$

Mā te whakawehe ki te -17 ka wetekia te whakareanga ki te -17.

$$\sqrt{2x}=\frac{17y-5\pi ^{3}}{-17}$$

Whakawehe 17y-5\pi ^{3} ki te -17.

$$\sqrt{2x}=-y+\frac{5\pi ^{3}}{17}$$

Pūruatia ngā taha e rua o te whārite.

$$2x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{289}$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x}{2}=\frac{\left(5\pi ^{3}-17y\right)^{2}}{2\times 289}$$

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

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{2\times 289}$$

Whakawehe \frac{\left(-17y+5\pi ^{3}\right)^{2}}{289} ki te 2.

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

Whakaoti mō x (complex solution)

$$x=\frac{\left(5\pi ^{3}-17y\right)^{2}}{578}$$

$$arg(-\frac{y}{2}+\frac{5\pi ^{3}}{34})<\pi \text{ or }y=\frac{5\pi ^{3}}{17}$$

Whakaoti mō y (complex solution)

$$y=-\sqrt{2x}+\frac{5\pi ^{3}}{17}$$

Whakaoti mō y

$$y=-\sqrt{2x}+\frac{5\pi ^{3}}{17}$$

$$x\geq 0$$