36y=12+18:(-27y) eching

$$36 y = 12 + 18 : ( - 27 y )$$

y uchun yechish

$$y=\frac{\sqrt{3}}{18}+\frac{1}{6}\approx 0,262891712$$

$$y=-\frac{\sqrt{3}}{18}+\frac{1}{6}\approx 0,070441622$$

Kvadrat tenglamalaridan foydalanish qoidalari

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -27y ga ko'paytirish.

$$36y\left(-27\right)y=-27y\times 12+18$$

-972 hosil qilish uchun 36 va -27 ni ko'paytirish.

$$-972yy=-27y\times 12+18$$

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$-972y^{2}=-27y\times 12+18$$

-324 hosil qilish uchun -27 va 12 ni ko'paytirish.

$$-972y^{2}=-324y+18$$

324y ni ikki tarafga qo’shing.

$$-972y^{2}+324y=18$$

Ikkala tarafdan 18 ni ayirish.

$$-972y^{2}+324y-18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -972 ni a, 324 ni b va -18 ni c bilan almashtiring.

$$y=\frac{-324±\sqrt{324^{2}-4\left(-972\right)\left(-18\right)}}{2\left(-972\right)}$$

324 kvadratini chiqarish.

$$y=\frac{-324±\sqrt{104976-4\left(-972\right)\left(-18\right)}}{2\left(-972\right)}$$

-4 ni -972 marotabaga ko'paytirish.

$$y=\frac{-324±\sqrt{104976+3888\left(-18\right)}}{2\left(-972\right)}$$

3888 ni -18 marotabaga ko'paytirish.

$$y=\frac{-324±\sqrt{104976-69984}}{2\left(-972\right)}$$

104976 ni -69984 ga qo'shish.

$$y=\frac{-324±\sqrt{34992}}{2\left(-972\right)}$$

34992 ning kvadrat ildizini chiqarish.

$$y=\frac{-324±108\sqrt{3}}{2\left(-972\right)}$$

2 ni -972 marotabaga ko'paytirish.

$$y=\frac{-324±108\sqrt{3}}{-1944}$$

y=\frac{-324±108\sqrt{3}}{-1944} tenglamasini yeching, bunda ± musbat. -324 ni 108\sqrt{3} ga qo'shish.

$$y=\frac{108\sqrt{3}-324}{-1944}$$

-324+108\sqrt{3} ni -1944 ga bo'lish.

$$y=-\frac{\sqrt{3}}{18}+\frac{1}{6}$$

y=\frac{-324±108\sqrt{3}}{-1944} tenglamasini yeching, bunda ± manfiy. -324 dan 108\sqrt{3} ni ayirish.

$$y=\frac{-108\sqrt{3}-324}{-1944}$$

-324-108\sqrt{3} ni -1944 ga bo'lish.

$$y=\frac{\sqrt{3}}{18}+\frac{1}{6}$$

Tenglama yechildi.

$$y=-\frac{\sqrt{3}}{18}+\frac{1}{6} y=\frac{\sqrt{3}}{18}+\frac{1}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -27y ga ko'paytirish.

$$36y\left(-27\right)y=-27y\times 12+18$$

-972 hosil qilish uchun 36 va -27 ni ko'paytirish.

$$-972yy=-27y\times 12+18$$

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$-972y^{2}=-27y\times 12+18$$

-324 hosil qilish uchun -27 va 12 ni ko'paytirish.

$$-972y^{2}=-324y+18$$

324y ni ikki tarafga qo’shing.

$$-972y^{2}+324y=18$$

Ikki tarafini -972 ga bo‘ling.

$$\frac{-972y^{2}+324y}{-972}=\frac{18}{-972}$$

-972 ga bo'lish -972 ga ko'paytirishni bekor qiladi.

$$y^{2}+\frac{324}{-972}y=\frac{18}{-972}$$

\frac{324}{-972} ulushini 324 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$y^{2}-\frac{1}{3}y=\frac{18}{-972}$$

\frac{18}{-972} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$y^{2}-\frac{1}{3}y=-\frac{1}{54}$$

-\frac{1}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{6} olish uchun. Keyin, -\frac{1}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-\frac{1}{3}y+\left(-\frac{1}{6}\right)^{2}=-\frac{1}{54}+\left(-\frac{1}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{6} kvadratini chiqarish.

$$y^{2}-\frac{1}{3}y+\frac{1}{36}=-\frac{1}{54}+\frac{1}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{54} ni \frac{1}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$y^{2}-\frac{1}{3}y+\frac{1}{36}=\frac{1}{108}$$

y^{2}-\frac{1}{3}y+\frac{1}{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.

$$\left(y-\frac{1}{6}\right)^{2}=\frac{1}{108}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-\frac{1}{6}\right)^{2}}=\sqrt{\frac{1}{108}}$$

Qisqartirish.

$$y-\frac{1}{6}=\frac{\sqrt{3}}{18} y-\frac{1}{6}=-\frac{\sqrt{3}}{18}$$

\frac{1}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$y=\frac{\sqrt{3}}{18}+\frac{1}{6} y=-\frac{\sqrt{3}}{18}+\frac{1}{6}$$