y^2+4y+8y-12=0 eching

$$y ^ { 2 } + 4 y + 8 y - 12 = 0$$

y uchun yechish

$$y=4\sqrt{3}-6\approx 0,92820323$$

$$y=-4\sqrt{3}-6\approx -12,92820323$$

Kvadrat tenglamalaridan foydalanish qoidalari

12y ni olish uchun 4y va 8y ni birlashtirish.

$$y^{2}+12y-12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 12 ni b va -12 ni c bilan almashtiring.

$$y=\frac{-12±\sqrt{12^{2}-4\left(-12\right)}}{2}$$

12 kvadratini chiqarish.

$$y=\frac{-12±\sqrt{144-4\left(-12\right)}}{2}$$

-4 ni -12 marotabaga ko'paytirish.

$$y=\frac{-12±\sqrt{144+48}}{2}$$

144 ni 48 ga qo'shish.

$$y=\frac{-12±\sqrt{192}}{2}$$

192 ning kvadrat ildizini chiqarish.

$$y=\frac{-12±8\sqrt{3}}{2}$$

y=\frac{-12±8\sqrt{3}}{2} tenglamasini yeching, bunda ± musbat. -12 ni 8\sqrt{3} ga qo'shish.

$$y=\frac{8\sqrt{3}-12}{2}$$

-12+8\sqrt{3} ni 2 ga bo'lish.

$$y=4\sqrt{3}-6$$

y=\frac{-12±8\sqrt{3}}{2} tenglamasini yeching, bunda ± manfiy. -12 dan 8\sqrt{3} ni ayirish.

$$y=\frac{-8\sqrt{3}-12}{2}$$

-12-8\sqrt{3} ni 2 ga bo'lish.

$$y=-4\sqrt{3}-6$$

Tenglama yechildi.

$$y=4\sqrt{3}-6 y=-4\sqrt{3}-6$$

Kvadratni yakunlash bo'yicha qadamlar

12y ni olish uchun 4y va 8y ni birlashtirish.

$$y^{2}+12y-12=0$$

12 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$y^{2}+12y=12$$

12 ni bo‘lish, x shartining koeffitsienti, 2 ga 6 olish uchun. Keyin, 6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}+12y+6^{2}=12+6^{2}$$

6 kvadratini chiqarish.

$$y^{2}+12y+36=12+36$$

12 ni 36 ga qo'shish.

$$y^{2}+12y+36=48$$

y^{2}+12y+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y+6\right)^{2}=48$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y+6\right)^{2}}=\sqrt{48}$$

Qisqartirish.

$$y+6=4\sqrt{3} y+6=-4\sqrt{3}$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$y=4\sqrt{3}-6 y=-4\sqrt{3}-6$$