(x+1/3)^2+2x-5/2=1/9+x^2-2x-7/6+frac{4+3x}{3} eching

$$( x + \frac { 1 } { 3 } ) ^ { 2 } + \frac { 2 x - 5 } { 2 } = \frac { 1 } { 9 } + x ^ { 2 } - 2 x - \frac { 7 } { 6 } + \frac { 4 + 3 x } { 3 }$$

x uchun yechish

$$x=1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 18 ga, 2,9,6,3 ning eng kichik karralisiga ko‘paytiring.

$$18\left(x+\frac{1}{3}\right)^{2}+9\left(2x-5\right)=2+18x^{2}-36x-21+6\left(4+3x\right)$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+\frac{1}{3}\right)^{2} kengaytirilishi uchun ishlating.

$$18\left(x^{2}+\frac{2}{3}x+\frac{1}{9}\right)+9\left(2x-5\right)=2+18x^{2}-36x-21+6\left(4+3x\right)$$

18 ga x^{2}+\frac{2}{3}x+\frac{1}{9} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}+12x+2+9\left(2x-5\right)=2+18x^{2}-36x-21+6\left(4+3x\right)$$

9 ga 2x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}+12x+2+18x-45=2+18x^{2}-36x-21+6\left(4+3x\right)$$

30x ni olish uchun 12x va 18x ni birlashtirish.

$$18x^{2}+30x+2-45=2+18x^{2}-36x-21+6\left(4+3x\right)$$

-43 olish uchun 2 dan 45 ni ayirish.

$$18x^{2}+30x-43=2+18x^{2}-36x-21+6\left(4+3x\right)$$

-19 olish uchun 2 dan 21 ni ayirish.

$$18x^{2}+30x-43=-19+18x^{2}-36x+6\left(4+3x\right)$$

6 ga 4+3x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}+30x-43=-19+18x^{2}-36x+24+18x$$

5 olish uchun -19 va 24'ni qo'shing.

$$18x^{2}+30x-43=5+18x^{2}-36x+18x$$

-18x ni olish uchun -36x va 18x ni birlashtirish.

$$18x^{2}+30x-43=5+18x^{2}-18x$$

Ikkala tarafdan 18x^{2} ni ayirish.

$$18x^{2}+30x-43-18x^{2}=5-18x$$

0 ni olish uchun 18x^{2} va -18x^{2} ni birlashtirish.

$$30x-43=5-18x$$

18x ni ikki tarafga qo’shing.

$$30x-43+18x=5$$

48x ni olish uchun 30x va 18x ni birlashtirish.

$$48x-43=5$$

43 ni ikki tarafga qo’shing.

$$48x=5+43$$

48 olish uchun 5 va 43'ni qo'shing.

$$48x=48$$

Ikki tarafini 48 ga bo‘ling.

$$x=\frac{48}{48}$$

1 ni olish uchun 48 ni 48 ga bo‘ling.

$$x=1$$