(x^2-3)sqrt{2x+y}=0 eching

$$( { x }^{ 2 } -3) \sqrt{ 2x+y } =0$$

y uchun yechish

$$\left\{\begin{matrix}\\y=-2x\text{, }&\text{unconditionally}\\y\geq -2x\text{, }&|x|=\sqrt{3}\end{matrix}\right,$$

Ildizli tenglamalarni yechish qadamlari

Ikki tarafini x^{2}-3 ga bo‘ling.

$$\frac{\left(x^{2}-3\right)\sqrt{y+2x}}{x^{2}-3}=\frac{0}{x^{2}-3}$$

x^{2}-3 ga bo'lish x^{2}-3 ga ko'paytirishni bekor qiladi.

$$\sqrt{y+2x}=\frac{0}{x^{2}-3}$$

0 ni x^{2}-3 ga bo'lish.

$$\sqrt{y+2x}=0$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$y+2x=0$$

Tenglamaning ikkala tarafidan 2x ni ayirish.

$$y+2x-2x=-2x$$

O‘zidan 2x ayirilsa 0 qoladi.

$$y=-2x$$

x uchun yechish (complex solution)

$$x=-\sqrt{3}\approx -1,732050808$$

$$x=\sqrt{3}\approx 1,732050808$$

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

y uchun yechish (complex solution)

$$\left\{\begin{matrix}\\y=-2x\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=-\sqrt{3}\text{ or }x=\sqrt{3}\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}\\x=-\frac{y}{2}\text{, }&\text{unconditionally}\\x=-\sqrt{3}\text{, }&y\geq 2\sqrt{3}\\x=\sqrt{3}\approx 1,732050808\text{, }&y\geq -2\sqrt{3}\end{matrix}\right,$$