1/3x-2=2x-3 eching

$$\frac { 1 } { 3 x } - 2 = 2 x - 3$$

x uchun yechish

$$x=\frac{\sqrt{33}}{12}+\frac{1}{4}\approx 0,728713554$$

$$x=-\frac{\sqrt{33}}{12}+\frac{1}{4}\approx -0,228713554$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3x ga ko'paytirish.

$$1+3x\left(-2\right)=2x\times 3x+3x\left(-3\right)$$

-6 hosil qilish uchun 3 va -2 ni ko'paytirish.

$$1-6x=2x\times 3x+3x\left(-3\right)$$

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

$$1-6x=2x^{2}\times 3+3x\left(-3\right)$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

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

-9 hosil qilish uchun 3 va -3 ni ko'paytirish.

$$1-6x=6x^{2}-9x$$

Ikkala tarafdan 6x^{2} ni ayirish.

$$1-6x-6x^{2}=-9x$$

9x ni ikki tarafga qo’shing.

$$1-6x-6x^{2}+9x=0$$

3x ni olish uchun -6x va 9x ni birlashtirish.

$$1+3x-6x^{2}=0$$

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.

$$-6x^{2}+3x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -6 ni a, 3 ni b va 1 ni c bilan almashtiring.

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

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\left(-6\right)}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+24}}{2\left(-6\right)}$$

9 ni 24 ga qo'shish.

$$x=\frac{-3±\sqrt{33}}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{33}}{-12}$$

x=\frac{-3±\sqrt{33}}{-12} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{33} ga qo'shish.

$$x=\frac{\sqrt{33}-3}{-12}$$

-3+\sqrt{33} ni -12 ga bo'lish.

$$x=-\frac{\sqrt{33}}{12}+\frac{1}{4}$$

x=\frac{-3±\sqrt{33}}{-12} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{33} ni ayirish.

$$x=\frac{-\sqrt{33}-3}{-12}$$

-3-\sqrt{33} ni -12 ga bo'lish.

$$x=\frac{\sqrt{33}}{12}+\frac{1}{4}$$

Tenglama yechildi.

$$x=-\frac{\sqrt{33}}{12}+\frac{1}{4} x=\frac{\sqrt{33}}{12}+\frac{1}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3x ga ko'paytirish.

$$1+3x\left(-2\right)=2x\times 3x+3x\left(-3\right)$$

-6 hosil qilish uchun 3 va -2 ni ko'paytirish.

$$1-6x=2x\times 3x+3x\left(-3\right)$$

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

$$1-6x=2x^{2}\times 3+3x\left(-3\right)$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

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

-9 hosil qilish uchun 3 va -3 ni ko'paytirish.

$$1-6x=6x^{2}-9x$$

Ikkala tarafdan 6x^{2} ni ayirish.

$$1-6x-6x^{2}=-9x$$

9x ni ikki tarafga qo’shing.

$$1-6x-6x^{2}+9x=0$$

3x ni olish uchun -6x va 9x ni birlashtirish.

$$1+3x-6x^{2}=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$3x-6x^{2}=-1$$

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

$$-6x^{2}+3x=-1$$

Ikki tarafini -6 ga bo‘ling.

$$\frac{-6x^{2}+3x}{-6}=-\frac{1}{-6}$$

-6 ga bo'lish -6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{3}{-6}x=-\frac{1}{-6}$$

\frac{3}{-6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1}{2}x=-\frac{1}{-6}$$

-1 ni -6 ga bo'lish.

$$x^{2}-\frac{1}{2}x=\frac{1}{6}$$

-\frac{1}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{4} olish uchun. Keyin, -\frac{1}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=\frac{1}{6}+\left(-\frac{1}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{4} kvadratini chiqarish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{1}{6}+\frac{1}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{6} ni \frac{1}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{11}{48}$$

x^{2}-\frac{1}{2}x+\frac{1}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{11}{48}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{11}{48}}$$

Qisqartirish.

$$x-\frac{1}{4}=\frac{\sqrt{33}}{12} x-\frac{1}{4}=-\frac{\sqrt{33}}{12}$$

\frac{1}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{33}}{12}+\frac{1}{4} x=-\frac{\sqrt{33}}{12}+\frac{1}{4}$$