Whakaoti i te x^frac{5{3}}+y5/3=1000

$$x ^ { \frac { 5 } { 3 } } + y \frac { 5 } { 3 } = 1000$$

Whakaoti mō y

$$y=-\frac{3x^{\frac{5}{3}}}{5}+600$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$y\times \frac{5}{3}=1000-x^{\frac{5}{3}}$$

He hanga arowhānui tō te whārite.

$$\frac{5}{3}y=1000-x^{\frac{5}{3}}$$

Whakawehea ngā taha e rua o te whārite ki te \frac{5}{3}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{5}{3}y}{\frac{5}{3}}=\frac{1000-x^{\frac{5}{3}}}{\frac{5}{3}}$$

Mā te whakawehe ki te \frac{5}{3} ka wetekia te whakareanga ki te \frac{5}{3}.

$$y=\frac{1000-x^{\frac{5}{3}}}{\frac{5}{3}}$$

Whakawehe 1000-x^{\frac{5}{3}} ki te \frac{5}{3} mā te whakarea 1000-x^{\frac{5}{3}} ki te tau huripoki o \frac{5}{3}.

$$y=-\frac{3x^{\frac{5}{3}}}{5}+600$$

Whakaoti mō x (complex solution)

$$x=\frac{125\left(600-y\right)^{3}}{27}$$

$$y=600\text{ or }arg(-\frac{5y}{3}+1000)<\frac{2\pi }{3}$$

Whakaoti mō x

$$x=\frac{3^{\frac{2}{5}}\left(3000-5y\right)^{\frac{3}{5}}}{3}$$