2left(x+1right)^2-left(x-2right)^2=xleft(x-3right) eching

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

x uchun yechish

$$x=\frac{2}{11}\approx 0,181818182$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

2 ga x^{2}+2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

x^{2}-4x+4 teskarisini topish uchun har birining teskarisini toping.

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

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

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

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

$$x^{2}+8x+2-4=x\left(x-3\right)$$

-2 olish uchun 2 dan 4 ni ayirish.

$$x^{2}+8x-2=x\left(x-3\right)$$

x ga x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+8x-2=x^{2}-3x$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}+8x-2-x^{2}=-3x$$

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

$$8x-2=-3x$$

3x ni ikki tarafga qo’shing.

$$8x-2+3x=0$$

11x ni olish uchun 8x va 3x ni birlashtirish.

$$11x-2=0$$

2 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$11x=2$$

Ikki tarafini 11 ga bo‘ling.

$$x=\frac{2}{11}$$