y=1/2sqrt{x-1} eching

$$y= \frac{ 1 }{ 2 } \sqrt{ x-1 }$$

x uchun yechish

$$x=4y^{2}+1$$

$$y\geq 0$$

Ildizli tenglamalarni yechish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1}{2}\sqrt{x-1}=y$$

Ikkala tarafini 2 ga ko‘paytiring.

$$\frac{\frac{1}{2}\sqrt{x-1}}{\frac{1}{2}}=\frac{y}{\frac{1}{2}}$$

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

$$\sqrt{x-1}=\frac{y}{\frac{1}{2}}$$

y ni \frac{1}{2} ga bo'lish y ga k'paytirish \frac{1}{2} ga qaytarish.

$$\sqrt{x-1}=2y$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x-1=4y^{2}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x-1-\left(-1\right)=4y^{2}-\left(-1\right)$$

O‘zidan -1 ayirilsa 0 qoladi.

$$x=4y^{2}-\left(-1\right)$$

4y^{2} dan -1 ni ayirish.

$$x=4y^{2}+1$$

x uchun yechish (complex solution)

$$x=4y^{2}+1$$

$$arg(y)<\pi \text{ or }y=0$$

y uchun yechish (complex solution)

$$y=\frac{\sqrt{x-1}}{2}$$

y uchun yechish

$$y=\frac{\sqrt{x-1}}{2}$$

$$x\geq 1$$