(12+x)*(12-x)=108 eching

$$( 12 + x ) \times ( 12 - x ) = 108$$

x uchun yechish

$$x=6$$

$$x=-6$$

Kvadrat ildizini topish bo'yicha qadamlar

Hisoblang: \left(12+x\right)\left(12-x\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 12 kvadratini chiqarish.

$$144-x^{2}=108$$

Ikkala tarafdan 144 ni ayirish.

$$-x^{2}=108-144$$

-36 olish uchun 108 dan 144 ni ayirish.

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

Ikki tarafini -1 ga bo‘ling.

$$x^{2}=\frac{-36}{-1}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-36}{-1} kasrini 36 ga soddalashtirish mumkin.

$$x^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=6 x=-6$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(12+x\right)\left(12-x\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 12 kvadratini chiqarish.

$$144-x^{2}=108$$

Ikkala tarafdan 108 ni ayirish.

$$144-x^{2}-108=0$$

36 olish uchun 144 dan 108 ni ayirish.

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

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 0 ni b va 36 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 36}}{2\left(-1\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 36}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{4\times 36}}{2\left(-1\right)}$$

4 ni 36 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{144}}{2\left(-1\right)}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±12}{-2}$$

x=\frac{0±12}{-2} tenglamasini yeching, bunda ± musbat. 12 ni -2 ga bo'lish.

$$x=-6$$

x=\frac{0±12}{-2} tenglamasini yeching, bunda ± manfiy. -12 ni -2 ga bo'lish.

$$x=6$$

Tenglama yechildi.

$$x=-6 x=6$$