x=frac{sqrt{a+bx}}{t} eching

$$x = \frac { \sqrt { a + b x } } { t }$$

a uchun yechish

$$a=x\left(xt^{2}-b\right)$$

$$\left(x\leq 0\text{ and }t<0\right)\text{ or }\left(x\geq 0\text{ and }t>0\right)$$

Ildizli tenglamalarni yechish qadamlari

Tenglamaning ikkala tarafini t ga ko'paytirish.

$$xt=\sqrt{a+bx}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\sqrt{a+bx}=xt$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$a+bx=t^{2}x^{2}$$

Tenglamaning ikkala tarafidan bx ni ayirish.

$$a+bx-bx=t^{2}x^{2}-bx$$

O‘zidan bx ayirilsa 0 qoladi.

$$a=t^{2}x^{2}-bx$$

x^{2}t^{2} dan bx ni ayirish.

$$a=x\left(xt^{2}-b\right)$$

b uchun yechish

$$\left\{\begin{matrix}b=\frac{\left(tx\right)^{2}-a}{x}\text{, }&\left(x<0\text{ and }t<0\right)\text{ or }\left(x>0\text{ and }t>0\right)\\b\in \mathrm{R}\text{, }&x=0\text{ and }a=0\text{ and }t\neq 0\end{matrix}\right,$$

Ildizli tenglamalarni yechish qadamlari

Tenglamaning ikkala tarafini t ga ko'paytirish.

$$xt=\sqrt{a+bx}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\sqrt{a+bx}=xt$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$xb+a=t^{2}x^{2}$$

Tenglamaning ikkala tarafidan a ni ayirish.

$$xb+a-a=t^{2}x^{2}-a$$

O‘zidan a ayirilsa 0 qoladi.

$$xb=t^{2}x^{2}-a$$

Ikki tarafini x ga bo‘ling.

$$\frac{xb}{x}=\frac{t^{2}x^{2}-a}{x}$$

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

$$b=\frac{t^{2}x^{2}-a}{x}$$

x^{2}t^{2}-a ni x ga bo'lish.

$$b=xt^{2}-\frac{a}{x}$$

a uchun yechish (complex solution)

$$a=x\left(xt^{2}-b\right)$$

$$\left(x=0\text{ or }arg(tx)<\pi \right)\text{ and }t\neq 0$$

b uchun yechish (complex solution)

$$\left\{\begin{matrix}b=\frac{\left(tx\right)^{2}-a}{x}\text{, }&arg(tx)<\pi \text{ and }t\neq 0\text{ and }x\neq 0\\b\in \mathrm{C}\text{, }&a=0\text{ and }x=0\text{ and }t\neq 0\end{matrix}\right,$$