(1/2-x)^2+3x=1/4+x(x+2) eching

$$( \frac { 1 } { 2 } - x ) ^ { 2 } + 3 x = \frac { 1 } { 4 } + x ( x + 2 )$$

x uchun yechish (complex solution)

$$x\in \mathrm{C}$$

Yechim qadamlari

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

$$\frac{1}{4}-x+x^{2}+3x=\frac{1}{4}+x\left(x+2\right)$$

2x ni olish uchun -x va 3x ni birlashtirish.

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

x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan \frac{1}{4} ni ayirish.

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

0 olish uchun \frac{1}{4} dan \frac{1}{4} ni ayirish.

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

Ikkala tarafdan x^{2} ni ayirish.

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

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$2x=2x$$

Ikkala tarafdan 2x ni ayirish.

$$2x-2x=0$$

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

$$0=0$$

0 va 0 ni taqqoslang.

$$\text{true}$$

Bu har qanday x uchun to‘g‘ri.

$$x\in \mathrm{C}$$

x uchun yechish

$$x\in \mathrm{R}$$

Yechim qadamlari

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

$$\frac{1}{4}-x+x^{2}+3x=\frac{1}{4}+x\left(x+2\right)$$

2x ni olish uchun -x va 3x ni birlashtirish.

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

x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan \frac{1}{4} ni ayirish.

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

0 olish uchun \frac{1}{4} dan \frac{1}{4} ni ayirish.

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

Ikkala tarafdan x^{2} ni ayirish.

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

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$2x=2x$$

Ikkala tarafdan 2x ni ayirish.

$$2x-2x=0$$

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

$$0=0$$

0 va 0 ni taqqoslang.

$$\text{true}$$

Bu har qanday x uchun to‘g‘ri.

$$x\in \mathrm{R}$$