v^2=u^2+2gh eching

$${ v }^{ 2 } = { u }^{ 2 } +2gh$$

g uchun yechish

$$\left\{\begin{matrix}g=-\frac{u^{2}-v^{2}}{2h}\text{, }&h\neq 0\\g\in \mathrm{R}\text{, }&h=0\text{ and }|v|=|u|\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$u^{2}+2gh=v^{2}$$

Ikkala tarafdan u^{2} ni ayirish.

$$2gh=v^{2}-u^{2}$$

Tenglama standart shaklda.

$$2hg=v^{2}-u^{2}$$

Ikki tarafini 2h ga bo‘ling.

$$\frac{2hg}{2h}=\frac{\left(v-u\right)\left(u+v\right)}{2h}$$

2h ga bo'lish 2h ga ko'paytirishni bekor qiladi.

$$g=\frac{\left(v-u\right)\left(u+v\right)}{2h}$$

h uchun yechish

$$\left\{\begin{matrix}h=-\frac{u^{2}-v^{2}}{2g}\text{, }&g\neq 0\\h\in \mathrm{R}\text{, }&g=0\text{ and }|v|=|u|\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$u^{2}+2gh=v^{2}$$

Ikkala tarafdan u^{2} ni ayirish.

$$2gh=v^{2}-u^{2}$$

Ikki tarafini 2g ga bo‘ling.

$$\frac{2gh}{2g}=\frac{\left(v-u\right)\left(u+v\right)}{2g}$$

2g ga bo'lish 2g ga ko'paytirishni bekor qiladi.

$$h=\frac{\left(v-u\right)\left(u+v\right)}{2g}$$