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.

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

Ikki tarafini -2h ga bo‘ling.

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

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

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

\left(v+u\right)\left(v-u\right) ni -2h ga bo'lish.

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

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.

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

Tenglama standart shaklda.

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

Ikki tarafini -2g ga bo‘ling.

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

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

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

\left(v+u\right)\left(v-u\right) ni -2g ga bo'lish.

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