4x^2-6=4x eching

$$4 x ^ { 2 } - 6 = 4 x$$

x uchun yechish

$$x = \frac{\sqrt{7} + 1}{2} \approx 1,822875656$$

$$x=\frac{1-\sqrt{7}}{2}\approx -0,822875656$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 4x ni ayirish.

$$4x^{2}-6-4x=0$$

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.

$$4x^{2}-4x-6=0$$

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

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

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 4\left(-6\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-16\left(-6\right)}}{2\times 4}$$

-16 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+96}}{2\times 4}$$

16 ni 96 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{112}}{2\times 4}$$

112 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±4\sqrt{7}}{2\times 4}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±4\sqrt{7}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{4±4\sqrt{7}}{8}$$

x=\frac{4±4\sqrt{7}}{8} tenglamasini yeching, bunda ± musbat. 4 ni 4\sqrt{7} ga qo'shish.

$$x=\frac{4\sqrt{7}+4}{8}$$

4+4\sqrt{7} ni 8 ga bo'lish.

$$x=\frac{\sqrt{7}+1}{2}$$

x=\frac{4±4\sqrt{7}}{8} tenglamasini yeching, bunda ± manfiy. 4 dan 4\sqrt{7} ni ayirish.

$$x=\frac{4-4\sqrt{7}}{8}$$

4-4\sqrt{7} ni 8 ga bo'lish.

$$x=\frac{1-\sqrt{7}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{7}+1}{2} x=\frac{1-\sqrt{7}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 4x ni ayirish.

$$4x^{2}-6-4x=0$$

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

$$4x^{2}-4x=6$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-4x}{4}=\frac{6}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{4}{4}\right)x=\frac{6}{4}$$

-4 ni 4 ga bo'lish.

$$x^{2}-x=\frac{6}{4}$$

\frac{6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=\frac{3}{2}+\frac{1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-x+\frac{1}{4}=\frac{7}{4}$$

x^{2}-x+\frac{1}{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.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{7}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{7}{4}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{\sqrt{7}}{2} x-\frac{1}{2}=-\frac{\sqrt{7}}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{7}+1}{2} x=\frac{1-\sqrt{7}}{2}$$