sqrt{3/4x-6}=y eching

$$\sqrt { \frac { 3 } { 4 } x - 6 } = y$$

x uchun yechish

$$x=\frac{4\left(y^{2}+6\right)}{3}$$

$$y\geq 0$$

Ildizli tenglamalarni yechish qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\frac{3}{4}x-6=y^{2}$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$\frac{3}{4}x-6-\left(-6\right)=y^{2}-\left(-6\right)$$

O‘zidan -6 ayirilsa 0 qoladi.

$$\frac{3}{4}x=y^{2}-\left(-6\right)$$

y^{2} dan -6 ni ayirish.

$$\frac{3}{4}x=y^{2}+6$$

Tenglamaning ikki tarafini \frac{3}{4} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{\frac{3}{4}x}{\frac{3}{4}}=\frac{y^{2}+6}{\frac{3}{4}}$$

\frac{3}{4} ga bo'lish \frac{3}{4} ga ko'paytirishni bekor qiladi.

$$x=\frac{y^{2}+6}{\frac{3}{4}}$$

y^{2}+6 ni \frac{3}{4} ga bo'lish y^{2}+6 ga k'paytirish \frac{3}{4} ga qaytarish.

$$x=\frac{4y^{2}}{3}+8$$

x uchun yechish (complex solution)

$$x=\frac{4\left(y^{2}+6\right)}{3}$$

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

y uchun yechish (complex solution)

$$y=\frac{\sqrt{3\left(x-8\right)}}{2}$$

y uchun yechish

$$y=\frac{\sqrt{3\left(x-8\right)}}{2}$$

$$x\geq 8$$