(2x-1)(1+2x)+3(x+2)(x-2)=7(x-1)^2 eching

$$( 2 x - 1 ) ( 1 + 2 x ) + 3 ( x + 2 ) ( x - 2 ) = 7 ( x - 1 ) ^ { 2 }$$

x uchun yechish

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1,428571429$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$4x^{2}-1+3\left(x+2\right)\left(x-2\right)=7\left(x-1\right)^{2}$$

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

$$4x^{2}-1+\left(3x+6\right)\left(x-2\right)=7\left(x-1\right)^{2}$$

3x+6 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4x^{2}-1+3x^{2}-12=7\left(x-1\right)^{2}$$

7x^{2} ni olish uchun 4x^{2} va 3x^{2} ni birlashtirish.

$$7x^{2}-1-12=7\left(x-1\right)^{2}$$

-13 olish uchun -1 dan 12 ni ayirish.

$$7x^{2}-13=7\left(x-1\right)^{2}$$

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

$$7x^{2}-13=7\left(x^{2}-2x+1\right)$$

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

$$7x^{2}-13=7x^{2}-14x+7$$

Ikkala tarafdan 7x^{2} ni ayirish.

$$7x^{2}-13-7x^{2}=-14x+7$$

0 ni olish uchun 7x^{2} va -7x^{2} ni birlashtirish.

$$-13=-14x+7$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-14x+7=-13$$

Ikkala tarafdan 7 ni ayirish.

$$-14x=-13-7$$

-20 olish uchun -13 dan 7 ni ayirish.

$$-14x=-20$$

Ikki tarafini -14 ga bo‘ling.

$$x=\frac{-20}{-14}$$

\frac{-20}{-14} ulushini -2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{10}{7}$$