4x^2-2yx+25=left(2x-5right)^2 eching

$$4 { x }^{ 2 } -2yx+25= { \left(2x-5 \right) }^{ 2 }$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=10\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-5\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$4x^{2}-2yx+25-4x^{2}=-20x+25$$

0 ni olish uchun 4x^{2} va -4x^{2} ni birlashtirish.

$$-2yx+25=-20x+25$$

20x ni ikki tarafga qo’shing.

$$-2yx+25+20x=25$$

Ikkala tarafdan 25 ni ayirish.

$$-2yx+20x=25-25$$

0 olish uchun 25 dan 25 ni ayirish.

$$-2yx+20x=0$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-2y+20\right)x=0$$

Tenglama standart shaklda.

$$\left(20-2y\right)x=0$$

0 ni -2y+20 ga bo'lish.

$$x=0$$

y uchun yechish (complex solution)

$$\left\{\begin{matrix}\\y=10\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-5\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$-2yx+25=4x^{2}-20x+25-4x^{2}$$

0 ni olish uchun 4x^{2} va -4x^{2} ni birlashtirish.

$$-2yx+25=-20x+25$$

Ikkala tarafdan 25 ni ayirish.

$$-2yx=-20x+25-25$$

0 olish uchun 25 dan 25 ni ayirish.

$$-2yx=-20x$$

Tenglama standart shaklda.

$$\left(-2x\right)y=-20x$$

Ikki tarafini -2x ga bo‘ling.

$$\frac{\left(-2x\right)y}{-2x}=-\frac{20x}{-2x}$$

-2x ga bo'lish -2x ga ko'paytirishni bekor qiladi.

$$y=-\frac{20x}{-2x}$$

-20x ni -2x ga bo'lish.

$$y=10$$

x uchun yechish

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=10\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-5\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$4x^{2}-2yx+25-4x^{2}=-20x+25$$

0 ni olish uchun 4x^{2} va -4x^{2} ni birlashtirish.

$$-2yx+25=-20x+25$$

20x ni ikki tarafga qo’shing.

$$-2yx+25+20x=25$$

Ikkala tarafdan 25 ni ayirish.

$$-2yx+20x=25-25$$

0 olish uchun 25 dan 25 ni ayirish.

$$-2yx+20x=0$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-2y+20\right)x=0$$

Tenglama standart shaklda.

$$\left(20-2y\right)x=0$$

0 ni -2y+20 ga bo'lish.

$$x=0$$

y uchun yechish

$$\left\{\begin{matrix}\\y=10\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-5\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$-2yx+25=4x^{2}-20x+25-4x^{2}$$

0 ni olish uchun 4x^{2} va -4x^{2} ni birlashtirish.

$$-2yx+25=-20x+25$$

Ikkala tarafdan 25 ni ayirish.

$$-2yx=-20x+25-25$$

0 olish uchun 25 dan 25 ni ayirish.

$$-2yx=-20x$$

Tenglama standart shaklda.

$$\left(-2x\right)y=-20x$$

Ikki tarafini -2x ga bo‘ling.

$$\frac{\left(-2x\right)y}{-2x}=-\frac{20x}{-2x}$$

-2x ga bo'lish -2x ga ko'paytirishni bekor qiladi.

$$y=-\frac{20x}{-2x}$$

-20x ni -2x ga bo'lish.

$$y=10$$