sqrt{3x+1}+1=3x eching

$$\sqrt { 3 x + 1 } + 1 = 3 x$$

x uchun yechish

$$x=1$$

Yechim qadamlari

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$\sqrt{3x+1}=3x-1$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{3x+1}\right)^{2}=\left(3x-1\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{3x+1} ga hisoblang va 3x+1 ni qiymatni oling.

$$3x+1=\left(3x-1\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-1\right)^{2} kengaytirilishi uchun ishlating.

$$3x+1=9x^{2}-6x+1$$

Ikkala tarafdan 9x^{2} ni ayirish.

$$3x+1-9x^{2}=-6x+1$$

6x ni ikki tarafga qo’shing.

$$3x+1-9x^{2}+6x=1$$

9x ni olish uchun 3x va 6x ni birlashtirish.

$$9x+1-9x^{2}=1$$

Ikkala tarafdan 1 ni ayirish.

$$9x+1-9x^{2}-1=0$$

0 olish uchun 1 dan 1 ni ayirish.

$$9x-9x^{2}=0$$

x omili.

$$x\left(9-9x\right)=0$$

Tenglamani yechish uchun x=0 va 9-9x=0 ni yeching.

$$x=0 x=1$$

\sqrt{3x+1}+1=3x tenglamasida x uchun 0 ni almashtiring.

$$\sqrt{3\times 0+1}+1=3\times 0$$

Qisqartirish. x=0 qiymati bu tenglamani qoniqtirmaydi.

$$2=0$$

\sqrt{3x+1}+1=3x tenglamasida x uchun 1 ni almashtiring.

$$\sqrt{3\times 1+1}+1=3\times 1$$

Qisqartirish. x=1 tenglamani qoniqtiradi.

$$3=3$$

\sqrt{3x+1}=3x-1 tenglamasi noyob yechimga ega.

$$x=1$$