y^2/2-2y+2=6y eching

$$\frac { y ^ { 2 } } { 2 } - 2 y + 2 = 6 y$$

y uchun yechish

$$y=2\sqrt{15}+8\approx 15,745966692$$

$$y=8-2\sqrt{15}\approx 0,254033308$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

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

Ikkala tarafdan 12y ni ayirish.

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

-16y ni olish uchun -4y va -12y ni birlashtirish.

$$y^{2}-16y+4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -16 ni b va 4 ni c bilan almashtiring.

$$y=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 4}}{2}$$

-16 kvadratini chiqarish.

$$y=\frac{-\left(-16\right)±\sqrt{256-4\times 4}}{2}$$

-4 ni 4 marotabaga ko'paytirish.

$$y=\frac{-\left(-16\right)±\sqrt{256-16}}{2}$$

256 ni -16 ga qo'shish.

$$y=\frac{-\left(-16\right)±\sqrt{240}}{2}$$

240 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-16\right)±4\sqrt{15}}{2}$$

-16 ning teskarisi 16 ga teng.

$$y=\frac{16±4\sqrt{15}}{2}$$

y=\frac{16±4\sqrt{15}}{2} tenglamasini yeching, bunda ± musbat. 16 ni 4\sqrt{15} ga qo'shish.

$$y=\frac{4\sqrt{15}+16}{2}$$

16+4\sqrt{15} ni 2 ga bo'lish.

$$y=2\sqrt{15}+8$$

y=\frac{16±4\sqrt{15}}{2} tenglamasini yeching, bunda ± manfiy. 16 dan 4\sqrt{15} ni ayirish.

$$y=\frac{16-4\sqrt{15}}{2}$$

16-4\sqrt{15} ni 2 ga bo'lish.

$$y=8-2\sqrt{15}$$

Tenglama yechildi.

$$y=2\sqrt{15}+8 y=8-2\sqrt{15}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

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

Ikkala tarafdan 12y ni ayirish.

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

-16y ni olish uchun -4y va -12y ni birlashtirish.

$$y^{2}-16y+4=0$$

Ikkala tarafdan 4 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$y^{2}-16y=-4$$

-16 ni bo‘lish, x shartining koeffitsienti, 2 ga -8 olish uchun. Keyin, -8 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-16y+\left(-8\right)^{2}=-4+\left(-8\right)^{2}$$

-8 kvadratini chiqarish.

$$y^{2}-16y+64=-4+64$$

-4 ni 64 ga qo'shish.

$$y^{2}-16y+64=60$$

y^{2}-16y+64 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-8\right)^{2}=60$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-8\right)^{2}}=\sqrt{60}$$

Qisqartirish.

$$y-8=2\sqrt{15} y-8=-2\sqrt{15}$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$y=2\sqrt{15}+8 y=8-2\sqrt{15}$$