y=-sqrt{x+2}-3 eching

$$y = - \sqrt { x + 2 } - 3$$

x uchun yechish

$$x=\left(y+3\right)^{2}-2$$

$$-\left(y+3\right)\geq 0$$

Ildizli tenglamalarni yechish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-\sqrt{x+2}-3=y$$

3 ni ikki tarafga qo’shing.

$$-\sqrt{x+2}=y+3$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-\sqrt{x+2}}{-1}=\frac{y+3}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$\sqrt{x+2}=\frac{y+3}{-1}$$

y+3 ni -1 ga bo'lish.

$$\sqrt{x+2}=-\left(y+3\right)$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$x+2=\left(y+3\right)^{2}$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x+2-2=\left(y+3\right)^{2}-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$x=\left(y+3\right)^{2}-2$$

x uchun yechish (complex solution)

$$x=\left(y+3\right)^{2}-2$$

$$y=-3\text{ or }arg(y+3)\geq \pi$$

y uchun yechish (complex solution)

$$y=-\left(\sqrt{x+2}+3\right)$$

y uchun yechish

$$y=-\left(\sqrt{x+2}+3\right)$$

$$x\geq -2$$