x^frac{5{3}}+y5/3=1000 eching

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

y uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan x^{\frac{5}{3}} ni ayirish.

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

Tenglama standart shaklda.

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

Tenglamaning ikki tarafini \frac{5}{3} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

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

\frac{5}{3} ga bo'lish \frac{5}{3} ga ko'paytirishni bekor qiladi.

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

1000-x^{\frac{5}{3}} ni \frac{5}{3} ga bo'lish 1000-x^{\frac{5}{3}} ga k'paytirish \frac{5}{3} ga qaytarish.

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

x uchun yechish (complex solution)

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

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

x uchun yechish

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