w^2=3(w-1) eching

$${ w }^{ 2 } = 3(w-1)$$

w uchun yechish

$$w=\frac{3+\sqrt{3}i}{2}\approx 1,5+0,866025404i$$

$$w=\frac{-\sqrt{3}i+3}{2}\approx 1,5-0,866025404i$$

Kvadrat tenglamalaridan foydalanish qoidalari

3 ga w-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$w^{2}=3w-3$$

Ikkala tarafdan 3w ni ayirish.

$$w^{2}-3w=-3$$

3 ni ikki tarafga qo’shing.

$$w^{2}-3w+3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va 3 ni c bilan almashtiring.

$$w=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 3}}{2}$$

-3 kvadratini chiqarish.

$$w=\frac{-\left(-3\right)±\sqrt{9-4\times 3}}{2}$$

-4 ni 3 marotabaga ko'paytirish.

$$w=\frac{-\left(-3\right)±\sqrt{9-12}}{2}$$

9 ni -12 ga qo'shish.

$$w=\frac{-\left(-3\right)±\sqrt{-3}}{2}$$

-3 ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-3\right)±\sqrt{3}i}{2}$$

-3 ning teskarisi 3 ga teng.

$$w=\frac{3±\sqrt{3}i}{2}$$

w=\frac{3±\sqrt{3}i}{2} tenglamasini yeching, bunda ± musbat. 3 ni i\sqrt{3} ga qo'shish.

$$w=\frac{3+\sqrt{3}i}{2}$$

w=\frac{3±\sqrt{3}i}{2} tenglamasini yeching, bunda ± manfiy. 3 dan i\sqrt{3} ni ayirish.

$$w=\frac{-\sqrt{3}i+3}{2}$$

Tenglama yechildi.

$$w=\frac{3+\sqrt{3}i}{2} w=\frac{-\sqrt{3}i+3}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

3 ga w-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$w^{2}=3w-3$$

Ikkala tarafdan 3w ni ayirish.

$$w^{2}-3w=-3$$

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

$$w^{2}-3w+\left(-\frac{3}{2}\right)^{2}=-3+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$w^{2}-3w+\frac{9}{4}=-3+\frac{9}{4}$$

-3 ni \frac{9}{4} ga qo'shish.

$$w^{2}-3w+\frac{9}{4}=-\frac{3}{4}$$

w^{2}-3w+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(w-\frac{3}{2}\right)^{2}=-\frac{3}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w-\frac{3}{2}\right)^{2}}=\sqrt{-\frac{3}{4}}$$

Qisqartirish.

$$w-\frac{3}{2}=\frac{\sqrt{3}i}{2} w-\frac{3}{2}=-\frac{\sqrt{3}i}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$w=\frac{3+\sqrt{3}i}{2} w=\frac{-\sqrt{3}i+3}{2}$$