(6-2sqrt{x})^2+8x=6^2 eching

$$( 6 - 2 \sqrt { x } ) ^ { 2 } + 8 x = 6 ^ { 2 }$$

x uchun yechish

$$x=0$$

$$x=4$$

Yechim qadamlari

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$\left(6-2\sqrt{x}\right)^{2}+8x=36$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(6-2\sqrt{x}\right)^{2} kengaytirilishi uchun ishlating.

$$36-24\sqrt{x}+4\left(\sqrt{x}\right)^{2}+8x=36$$

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

$$36-24\sqrt{x}+4x+8x=36$$

12x ni olish uchun 4x va 8x ni birlashtirish.

$$36-24\sqrt{x}+12x=36$$

Ikkala tarafdan 36 ni ayirish.

$$-24\sqrt{x}+12x=36-36$$

0 olish uchun 36 dan 36 ni ayirish.

$$-24\sqrt{x}+12x=0$$

Tenglamaning ikkala tarafidan 12x ni ayirish.

$$-24\sqrt{x}=-12x$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(-24\sqrt{x}\right)^{2}=\left(-12x\right)^{2}$$

\left(-24\sqrt{x}\right)^{2} ni kengaytirish.

$$\left(-24\right)^{2}\left(\sqrt{x}\right)^{2}=\left(-12x\right)^{2}$$

2 daraja ko‘rsatkichini -24 ga hisoblang va 576 ni qiymatni oling.

$$576\left(\sqrt{x}\right)^{2}=\left(-12x\right)^{2}$$

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

$$576x=\left(-12x\right)^{2}$$

\left(-12x\right)^{2} ni kengaytirish.

$$576x=\left(-12\right)^{2}x^{2}$$

2 daraja ko‘rsatkichini -12 ga hisoblang va 144 ni qiymatni oling.

$$576x=144x^{2}$$

Ikkala tarafdan 144x^{2} ni ayirish.

$$576x-144x^{2}=0$$

x omili.

$$x\left(576-144x\right)=0$$

Tenglamani yechish uchun x=0 va 576-144x=0 ni yeching.

$$x=0 x=4$$

\left(6-2\sqrt{x}\right)^{2}+8x=6^{2} tenglamasida x uchun 0 ni almashtiring.

$$\left(6-2\sqrt{0}\right)^{2}+8\times 0=6^{2}$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$36=36$$

\left(6-2\sqrt{x}\right)^{2}+8x=6^{2} tenglamasida x uchun 4 ni almashtiring.

$$\left(6-2\sqrt{4}\right)^{2}+8\times 4=6^{2}$$

Qisqartirish. x=4 tenglamani qoniqtiradi.

$$36=36$$

-24\sqrt{x}=-12x boʻyicha barcha yechimlar roʻyxati.

$$x=0 x=4$$