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

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

x uchun yechish

$$x=\frac{3}{4}=0,75$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x-1 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

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

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

x^{2}+3x teskarisini topish uchun har birining teskarisini toping.

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

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

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

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

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

Hisoblang: \left(x-2\right)\left(x+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 2 kvadratini chiqarish.

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

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

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

x^{2}-2x+1 teskarisini topish uchun har birining teskarisini toping.

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

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

$$-2x-2=-4+2x-1$$

-5 olish uchun -4 dan 1 ni ayirish.

$$-2x-2=-5+2x$$

Ikkala tarafdan 2x ni ayirish.

$$-2x-2-2x=-5$$

-4x ni olish uchun -2x va -2x ni birlashtirish.

$$-4x-2=-5$$

2 ni ikki tarafga qo’shing.

$$-4x=-5+2$$

-3 olish uchun -5 va 2'ni qo'shing.

$$-4x=-3$$

Ikki tarafini -4 ga bo‘ling.

$$x=\frac{-3}{-4}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-3}{-4} kasrini \frac{3}{4} ga soddalashtirish mumkin.

$$x=\frac{3}{4}$$