y=sqrt{2x-4}-1 eching

$$y = \sqrt{ 2x-4 } -1$$

x uchun yechish

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

$$y+1\geq 0$$

Ildizli tenglamalarni yechish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\sqrt{2x-4}-1=y$$

1 ni ikki tarafga qo’shing.

$$\sqrt{2x-4}=y+1$$

Tenglamaning ikkala taraf kvadratini chiqarish.

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

4 ni tenglamaning ikkala tarafiga qo'shish.

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

O‘zidan -4 ayirilsa 0 qoladi.

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

\left(y+1\right)^{2} dan -4 ni ayirish.

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

Ikki tarafini 2 ga bo‘ling.

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

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

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

\left(y+1\right)^{2}+4 ni 2 ga bo'lish.

$$x=\frac{\left(y+1\right)^{2}}{2}+2$$

x uchun yechish (complex solution)

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

$$y=-1\text{ or }arg(y+1)<\pi$$

y uchun yechish (complex solution)

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

y uchun yechish

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

$$x\geq 2$$