F=gfrac{m_{1}m_{2}}{r^2} eching

$$F = g \frac { m _ { 1 } m _ { 2 } } { r ^ { 2 } }$$

g uchun yechish (complex solution)

$$\left\{\begin{matrix}g=\frac{Fr^{2}}{m_{1}m_{2}}\text{, }&m_{2}\neq 0\text{ and }m_{1}\neq 0\text{ and }r\neq 0\\g\in \mathrm{C}\text{, }&\left(m_{2}=0\text{ or }m_{1}=0\right)\text{ and }F=0\text{ and }r\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini r^{2} ga ko'paytirish.

$$Fr^{2}=gm_{1}m_{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$gm_{1}m_{2}=Fr^{2}$$

Tenglama standart shaklda.

$$m_{1}m_{2}g=Fr^{2}$$

Ikki tarafini m_{1}m_{2} ga bo‘ling.

$$\frac{m_{1}m_{2}g}{m_{1}m_{2}}=\frac{Fr^{2}}{m_{1}m_{2}}$$

m_{1}m_{2} ga bo'lish m_{1}m_{2} ga ko'paytirishni bekor qiladi.

$$g=\frac{Fr^{2}}{m_{1}m_{2}}$$

g uchun yechish

$$\left\{\begin{matrix}g=\frac{Fr^{2}}{m_{1}m_{2}}\text{, }&m_{2}\neq 0\text{ and }m_{1}\neq 0\text{ and }r\neq 0\\g\in \mathrm{R}\text{, }&\left(m_{2}=0\text{ or }m_{1}=0\right)\text{ and }F=0\text{ and }r\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini r^{2} ga ko'paytirish.

$$Fr^{2}=gm_{1}m_{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$gm_{1}m_{2}=Fr^{2}$$

Tenglama standart shaklda.

$$m_{1}m_{2}g=Fr^{2}$$

Ikki tarafini m_{1}m_{2} ga bo‘ling.

$$\frac{m_{1}m_{2}g}{m_{1}m_{2}}=\frac{Fr^{2}}{m_{1}m_{2}}$$

m_{1}m_{2} ga bo'lish m_{1}m_{2} ga ko'paytirishni bekor qiladi.

$$g=\frac{Fr^{2}}{m_{1}m_{2}}$$

F uchun yechish

$$F=\frac{gm_{1}m_{2}}{r^{2}}$$

$$r\neq 0$$