y=1/6*(1-(1-x/1)^3) eching

$$y = \frac { 1 } { 6 } \cdot ( 1 - ( 1 - \frac { x } { 1 } ) ^ { 3 } )$$

y uchun yechish

$$y=-\frac{x\left(-x^{2}+3x-3\right)}{6}$$

Yechim qadamlari

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$y=\frac{1}{6}\left(1-\left(1-x\right)^{3}\right)$$

\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} binom teoremasini \left(1-x\right)^{3} kengaytirilishi uchun ishlating.

$$y=\frac{1}{6}\left(1-\left(1+3\left(-x\right)+3\left(-x\right)^{2}+\left(-x\right)^{3}\right)\right)$$

2 daraja ko‘rsatkichini -x ga hisoblang va x^{2} ni qiymatni oling.

$$y=\frac{1}{6}\left(1-\left(1+3\left(-x\right)+3x^{2}+\left(-x\right)^{3}\right)\right)$$

1+3\left(-x\right)+3x^{2}+\left(-x\right)^{3} teskarisini topish uchun har birining teskarisini toping.

$$y=\frac{1}{6}\left(1-1-3\left(-x\right)-3x^{2}-\left(-x\right)^{3}\right)$$

0 olish uchun 1 dan 1 ni ayirish.

$$y=\frac{1}{6}\left(-3\left(-x\right)-3x^{2}-\left(-x\right)^{3}\right)$$

3 hosil qilish uchun -3 va -1 ni ko'paytirish.

$$y=\frac{1}{6}\left(3x-3x^{2}-\left(-x\right)^{3}\right)$$

\frac{1}{6} ga 3x-3x^{2}-\left(-x\right)^{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y=\frac{1}{2}x-\frac{1}{2}x^{2}-\frac{1}{6}\left(-x\right)^{3}$$

\left(-x\right)^{3} ni kengaytirish.

$$y=\frac{1}{2}x-\frac{1}{2}x^{2}-\frac{1}{6}\left(-1\right)^{3}x^{3}$$

3 daraja ko‘rsatkichini -1 ga hisoblang va -1 ni qiymatni oling.

$$y=\frac{1}{2}x-\frac{1}{2}x^{2}-\frac{1}{6}\left(-1\right)x^{3}$$

\frac{1}{6} hosil qilish uchun -\frac{1}{6} va -1 ni ko'paytirish.

$$y=\frac{1}{2}x-\frac{1}{2}x^{2}+\frac{1}{6}x^{3}$$

x uchun yechish

$$x=-\sqrt[3]{1-6y}+1$$