sqrt{2x+16}=2x+4 eching

$$\sqrt { 2 x + 16 } = 2 x + 4$$

x uchun yechish

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{2x+16}\right)^{2}=\left(2x+4\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{2x+16} ga hisoblang va 2x+16 ni qiymatni oling.

$$2x+16=\left(2x+4\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2x+4\right)^{2} kengaytirilishi uchun ishlating.

$$2x+16=4x^{2}+16x+16$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$2x+16-4x^{2}=16x+16$$

Ikkala tarafdan 16x ni ayirish.

$$2x+16-4x^{2}-16x=16$$

-14x ni olish uchun 2x va -16x ni birlashtirish.

$$-14x+16-4x^{2}=16$$

Ikkala tarafdan 16 ni ayirish.

$$-14x+16-4x^{2}-16=0$$

0 olish uchun 16 dan 16 ni ayirish.

$$-14x-4x^{2}=0$$

x omili.

$$x\left(-14-4x\right)=0$$

Tenglamani yechish uchun x=0 va -14-4x=0 ni yeching.

$$x=0 x=-\frac{7}{2}$$

\sqrt{2x+16}=2x+4 tenglamasida x uchun 0 ni almashtiring.

$$\sqrt{2\times 0+16}=2\times 0+4$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$4=4$$

\sqrt{2x+16}=2x+4 tenglamasida x uchun -\frac{7}{2} ni almashtiring.

$$\sqrt{2\left(-\frac{7}{2}\right)+16}=2\left(-\frac{7}{2}\right)+4$$

Qisqartirish. x=-\frac{7}{2} qiymati bu tenglamani qoniqtirmaydi, chunki oʻng va chap tarafdagi belgilar bir-biriga qarama-qarshi.

$$3=-3$$

\sqrt{2x+16}=2x+4 tenglamasi noyob yechimga ega.

$$x=0$$