sqrt{4x+1}=x+1 eching

$$\sqrt { 4 x + 1 } = x + 1$$

x uchun yechish

$$x=2$$

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{4x+1}\right)^{2}=\left(x+1\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{4x+1} ga hisoblang va 4x+1 ni qiymatni oling.

$$4x+1=\left(x+1\right)^{2}$$

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

$$4x+1=x^{2}+2x+1$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x+1-x^{2}=2x+1$$

Ikkala tarafdan 2x ni ayirish.

$$4x+1-x^{2}-2x=1$$

2x ni olish uchun 4x va -2x ni birlashtirish.

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

Ikkala tarafdan 1 ni ayirish.

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

0 olish uchun 1 dan 1 ni ayirish.

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

x omili.

$$x\left(2-x\right)=0$$

Tenglamani yechish uchun x=0 va 2-x=0 ni yeching.

$$x=0 x=2$$

\sqrt{4x+1}=x+1 tenglamasida x uchun 0 ni almashtiring.

$$\sqrt{4\times 0+1}=0+1$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$1=1$$

\sqrt{4x+1}=x+1 tenglamasida x uchun 2 ni almashtiring.

$$\sqrt{4\times 2+1}=2+1$$

Qisqartirish. x=2 tenglamani qoniqtiradi.

$$3=3$$

\sqrt{4x+1}=x+1 boʻyicha barcha yechimlar roʻyxati.

$$x=0 x=2$$