(x+2)^2/2+x^2-18/3=2x+2 eching

$$\frac { ( x + 2 ) ^ { 2 } } { 2 } + \frac { x ^ { 2 } - 18 } { 3 } = 2 x + 2$$

x uchun yechish

$$x = \frac{6 \sqrt{5}}{5} \approx 2,683281573$$

$$x = -\frac{6 \sqrt{5}}{5} \approx -2,683281573$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$3\left(x+2\right)^{2}+2\left(x^{2}-18\right)=12x+12$$

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

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

3 ga x^{2}+4x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+12x+12+2\left(x^{2}-18\right)=12x+12$$

2 ga x^{2}-18 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+12x+12+2x^{2}-36=12x+12$$

5x^{2} ni olish uchun 3x^{2} va 2x^{2} ni birlashtirish.

$$5x^{2}+12x+12-36=12x+12$$

-24 olish uchun 12 dan 36 ni ayirish.

$$5x^{2}+12x-24=12x+12$$

Ikkala tarafdan 12x ni ayirish.

$$5x^{2}+12x-24-12x=12$$

0 ni olish uchun 12x va -12x ni birlashtirish.

$$5x^{2}-24=12$$

24 ni ikki tarafga qo’shing.

$$5x^{2}=12+24$$

36 olish uchun 12 va 24'ni qo'shing.

$$5x^{2}=36$$

Ikki tarafini 5 ga bo‘ling.

$$x^{2}=\frac{36}{5}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{6\sqrt{5}}{5} x=-\frac{6\sqrt{5}}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$3\left(x+2\right)^{2}+2\left(x^{2}-18\right)=12x+12$$

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

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

3 ga x^{2}+4x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+12x+12+2\left(x^{2}-18\right)=12x+12$$

2 ga x^{2}-18 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+12x+12+2x^{2}-36=12x+12$$

5x^{2} ni olish uchun 3x^{2} va 2x^{2} ni birlashtirish.

$$5x^{2}+12x+12-36=12x+12$$

-24 olish uchun 12 dan 36 ni ayirish.

$$5x^{2}+12x-24=12x+12$$

Ikkala tarafdan 12x ni ayirish.

$$5x^{2}+12x-24-12x=12$$

0 ni olish uchun 12x va -12x ni birlashtirish.

$$5x^{2}-24=12$$

Ikkala tarafdan 12 ni ayirish.

$$5x^{2}-24-12=0$$

-36 olish uchun -24 dan 12 ni ayirish.

$$5x^{2}-36=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 0 ni b va -36 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-36\right)}}{2\times 5}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 5\left(-36\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-20\left(-36\right)}}{2\times 5}$$

-20 ni -36 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{720}}{2\times 5}$$

720 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12\sqrt{5}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±12\sqrt{5}}{10}$$

x=\frac{0±12\sqrt{5}}{10} tenglamasini yeching, bunda ± musbat.

$$x=\frac{6\sqrt{5}}{5}$$

x=\frac{0±12\sqrt{5}}{10} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{6\sqrt{5}}{5}$$

Tenglama yechildi.

$$x=\frac{6\sqrt{5}}{5} x=-\frac{6\sqrt{5}}{5}$$