F=GmM/r^2 eching

$$F = \frac { G m M } { r ^ { 2 } }$$

G uchun yechish (complex solution)

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$Fr^{2}=GmM$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$GmM=Fr^{2}$$

Tenglama standart shaklda.

$$MmG=Fr^{2}$$

Ikki tarafini mM ga bo‘ling.

$$\frac{MmG}{Mm}=\frac{Fr^{2}}{Mm}$$

mM ga bo'lish mM ga ko'paytirishni bekor qiladi.

$$G=\frac{Fr^{2}}{Mm}$$

G uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$Fr^{2}=GmM$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$GmM=Fr^{2}$$

Tenglama standart shaklda.

$$MmG=Fr^{2}$$

Ikki tarafini mM ga bo‘ling.

$$\frac{MmG}{Mm}=\frac{Fr^{2}}{Mm}$$

mM ga bo'lish mM ga ko'paytirishni bekor qiladi.

$$G=\frac{Fr^{2}}{Mm}$$

F uchun yechish

$$F=\frac{GMm}{r^{2}}$$

$$r\neq 0$$