1200x+400x=sqrt{3x} eching

$$1200 x + 400 x = \sqrt { 3 x }$$

x uchun yechish

$$x=\frac{3}{2560000}=0,000001172$$

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(1200x+400x\right)^{2}=\left(\sqrt{3x}\right)^{2}$$

1600x ni olish uchun 1200x va 400x ni birlashtirish.

$$\left(1600x\right)^{2}=\left(\sqrt{3x}\right)^{2}$$

\left(1600x\right)^{2} ni kengaytirish.

$$1600^{2}x^{2}=\left(\sqrt{3x}\right)^{2}$$

2 daraja ko‘rsatkichini 1600 ga hisoblang va 2560000 ni qiymatni oling.

$$2560000x^{2}=\left(\sqrt{3x}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{3x} ga hisoblang va 3x ni qiymatni oling.

$$2560000x^{2}=3x$$

Ikkala tarafdan 3x ni ayirish.

$$2560000x^{2}-3x=0$$

x omili.

$$x\left(2560000x-3\right)=0$$

Tenglamani yechish uchun x=0 va 2560000x-3=0 ni yeching.

$$x=0 x=\frac{3}{2560000}$$

1200x+400x=\sqrt{3x} tenglamasida x uchun 0 ni almashtiring.

$$1200\times 0+400\times 0=\sqrt{3\times 0}$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$0=0$$

1200x+400x=\sqrt{3x} tenglamasida x uchun \frac{3}{2560000} ni almashtiring.

$$1200\times \frac{3}{2560000}+400\times \frac{3}{2560000}=\sqrt{3\times \frac{3}{2560000}}$$

Qisqartirish. x=\frac{3}{2560000} tenglamani qoniqtiradi.

$$\frac{3}{1600}=\frac{3}{1600}$$

400x+1200x=\sqrt{3x} boʻyicha barcha yechimlar roʻyxati.

$$x=0 x=\frac{3}{2560000}$$