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

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

x uchun yechish

$$x=\frac{1}{4}=0,25$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2-3x\right)^{2} kengaytirilishi uchun ishlating.

$$4-12x+9x^{2}-\left(3x-1\right)\left(3x+1\right)=2$$

Hisoblang: \left(3x-1\right)\left(3x+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$4-12x+9x^{2}-\left(\left(3x\right)^{2}-1\right)=2$$

\left(3x\right)^{2} ni kengaytirish.

$$4-12x+9x^{2}-\left(3^{2}x^{2}-1\right)=2$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$4-12x+9x^{2}-\left(9x^{2}-1\right)=2$$

9x^{2}-1 teskarisini topish uchun har birining teskarisini toping.

$$4-12x+9x^{2}-9x^{2}+1=2$$

0 ni olish uchun 9x^{2} va -9x^{2} ni birlashtirish.

$$4-12x+1=2$$

5 olish uchun 4 va 1'ni qo'shing.

$$5-12x=2$$

Ikkala tarafdan 5 ni ayirish.

$$-12x=2-5$$

-3 olish uchun 2 dan 5 ni ayirish.

$$-12x=-3$$

Ikki tarafini -12 ga bo‘ling.

$$x=\frac{-3}{-12}$$

\frac{-3}{-12} ulushini -3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{4}$$