1/2by^2+nA_{s}y-nA_{s}d=0 eching

$$\frac { 1 } { 2 } b y ^ { 2 } + n A _ { s } y - n A _ { s } d = 0$$

A_s uchun yechish

$$\left\{\begin{matrix}A_{s}=-\frac{by^{2}}{2n\left(y-d\right)}\text{, }&y\neq d\text{ and }n\neq 0\\A_{s}\in \mathrm{R}\text{, }&\left(b=0\text{ and }y=d\right)\text{ or }\left(y=0\text{ and }d=0\right)\text{ or }\left(y=0\text{ and }n=0\text{ and }d\neq 0\right)\text{ or }\left(b=0\text{ and }n=0\text{ and }y\neq d\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan \frac{1}{2}by^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$nA_{s}y-nA_{s}d=-\frac{1}{2}by^{2}$$

A_{s}'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(ny-nd\right)A_{s}=-\frac{1}{2}by^{2}$$

Tenglama standart shaklda.

$$\left(ny-dn\right)A_{s}=-\frac{by^{2}}{2}$$

Ikki tarafini ny-nd ga bo‘ling.

$$\frac{\left(ny-dn\right)A_{s}}{ny-dn}=-\frac{\frac{by^{2}}{2}}{ny-dn}$$

ny-nd ga bo'lish ny-nd ga ko'paytirishni bekor qiladi.

$$A_{s}=-\frac{\frac{by^{2}}{2}}{ny-dn}$$

-\frac{by^{2}}{2} ni ny-nd ga bo'lish.

$$A_{s}=-\frac{by^{2}}{2n\left(y-d\right)}$$

b uchun yechish

$$\left\{\begin{matrix}b=-\frac{2A_{s}n\left(y-d\right)}{y^{2}}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&\left(n=0\text{ or }A_{s}=0\text{ or }d=0\right)\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

nA_{s}d ni ikki tarafga qo’shing.

$$\frac{1}{2}by^{2}+nA_{s}y=0+nA_{s}d$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{1}{2}by^{2}+nA_{s}y=nA_{s}d$$

Ikkala tarafdan nA_{s}y ni ayirish.

$$\frac{1}{2}by^{2}=nA_{s}d-nA_{s}y$$

Shartlarni qayta saralash.

$$\frac{1}{2}by^{2}=-A_{s}ny+A_{s}dn$$

Tenglama standart shaklda.

$$\frac{y^{2}}{2}b=A_{s}dn-A_{s}ny$$

Ikki tarafini \frac{1}{2}y^{2} ga bo‘ling.

$$\frac{2\times \frac{y^{2}}{2}b}{y^{2}}=\frac{2A_{s}n\left(d-y\right)}{y^{2}}$$

\frac{1}{2}y^{2} ga bo'lish \frac{1}{2}y^{2} ga ko'paytirishni bekor qiladi.

$$b=\frac{2A_{s}n\left(d-y\right)}{y^{2}}$$