3w^2-6w+2=0 eching

$$3 w ^ { 2 } - 6 w + 2 = 0$$

w uchun yechish

$$w=\frac{\sqrt{3}}{3}+1\approx 1,577350269$$

$$w=-\frac{\sqrt{3}}{3}+1\approx 0,422649731$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$3w^{2}-6w+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -6 ni b va 2 ni c bilan almashtiring.

$$w=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 3\times 2}}{2\times 3}$$

-6 kvadratini chiqarish.

$$w=\frac{-\left(-6\right)±\sqrt{36-4\times 3\times 2}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$w=\frac{-\left(-6\right)±\sqrt{36-12\times 2}}{2\times 3}$$

-12 ni 2 marotabaga ko'paytirish.

$$w=\frac{-\left(-6\right)±\sqrt{36-24}}{2\times 3}$$

36 ni -24 ga qo'shish.

$$w=\frac{-\left(-6\right)±\sqrt{12}}{2\times 3}$$

12 ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-6\right)±2\sqrt{3}}{2\times 3}$$

-6 ning teskarisi 6 ga teng.

$$w=\frac{6±2\sqrt{3}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$w=\frac{6±2\sqrt{3}}{6}$$

w=\frac{6±2\sqrt{3}}{6} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{3} ga qo'shish.

$$w=\frac{2\sqrt{3}+6}{6}$$

6+2\sqrt{3} ni 6 ga bo'lish.

$$w=\frac{\sqrt{3}}{3}+1$$

w=\frac{6±2\sqrt{3}}{6} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{3} ni ayirish.

$$w=\frac{6-2\sqrt{3}}{6}$$

6-2\sqrt{3} ni 6 ga bo'lish.

$$w=-\frac{\sqrt{3}}{3}+1$$

Tenglama yechildi.

$$w=\frac{\sqrt{3}}{3}+1 w=-\frac{\sqrt{3}}{3}+1$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$3w^{2}-6w+2=0$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$3w^{2}-6w+2-2=-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$3w^{2}-6w=-2$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3w^{2}-6w}{3}=-\frac{2}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

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

-6 ni 3 ga bo'lish.

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

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

$$w^{2}-2w+1=-\frac{2}{3}+1$$

-\frac{2}{3} ni 1 ga qo'shish.

$$w^{2}-2w+1=\frac{1}{3}$$

w^{2}-2w+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(w-1\right)^{2}=\frac{1}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w-1\right)^{2}}=\sqrt{\frac{1}{3}}$$

Qisqartirish.

$$w-1=\frac{\sqrt{3}}{3} w-1=-\frac{\sqrt{3}}{3}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$w=\frac{\sqrt{3}}{3}+1 w=-\frac{\sqrt{3}}{3}+1$$