1/3=m+m-1/m eching

$$\frac{1}{3}=m+\frac{m-1}{m}$$

m uchun yechish

$$m=\frac{\sqrt{10}-1}{3}\approx 0,72075922$$

$$m=\frac{-\sqrt{10}-1}{3}\approx -1,387425887$$

Kvadrat tenglamalaridan foydalanish qoidalari

m qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3m ga, 3,m ning eng kichik karralisiga ko‘paytiring.

$$m=3mm+3\left(m-1\right)$$

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

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

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

$$m=3m^{2}+3m-3$$

Ikkala tarafdan 3m^{2} ni ayirish.

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

Ikkala tarafdan 3m ni ayirish.

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

-2m ni olish uchun m va -3m ni birlashtirish.

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

3 ni ikki tarafga qo’shing.

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

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.

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

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

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

-2 kvadratini chiqarish.

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

-4 ni -3 marotabaga ko'paytirish.

$$m=\frac{-\left(-2\right)±\sqrt{4+12\times 3}}{2\left(-3\right)}$$

12 ni 3 marotabaga ko'paytirish.

$$m=\frac{-\left(-2\right)±\sqrt{4+36}}{2\left(-3\right)}$$

4 ni 36 ga qo'shish.

$$m=\frac{-\left(-2\right)±\sqrt{40}}{2\left(-3\right)}$$

40 ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-2\right)±2\sqrt{10}}{2\left(-3\right)}$$

-2 ning teskarisi 2 ga teng.

$$m=\frac{2±2\sqrt{10}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$m=\frac{2±2\sqrt{10}}{-6}$$

m=\frac{2±2\sqrt{10}}{-6} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{10} ga qo'shish.

$$m=\frac{2\sqrt{10}+2}{-6}$$

2+2\sqrt{10} ni -6 ga bo'lish.

$$m=\frac{-\sqrt{10}-1}{3}$$

m=\frac{2±2\sqrt{10}}{-6} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{10} ni ayirish.

$$m=\frac{2-2\sqrt{10}}{-6}$$

2-2\sqrt{10} ni -6 ga bo'lish.

$$m=\frac{\sqrt{10}-1}{3}$$

Tenglama yechildi.

$$m=\frac{-\sqrt{10}-1}{3} m=\frac{\sqrt{10}-1}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

m qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3m ga, 3,m ning eng kichik karralisiga ko‘paytiring.

$$m=3mm+3\left(m-1\right)$$

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

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

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

$$m=3m^{2}+3m-3$$

Ikkala tarafdan 3m^{2} ni ayirish.

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

Ikkala tarafdan 3m ni ayirish.

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

-2m ni olish uchun m va -3m ni birlashtirish.

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

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

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

Ikki tarafini -3 ga bo‘ling.

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

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

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

-2 ni -3 ga bo'lish.

$$m^{2}+\frac{2}{3}m=-\frac{3}{-3}$$

-3 ni -3 ga bo'lish.

$$m^{2}+\frac{2}{3}m=1$$

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{3} kvadratini chiqarish.

$$m^{2}+\frac{2}{3}m+\frac{1}{9}=1+\frac{1}{9}$$

1 ni \frac{1}{9} ga qo'shish.

$$m^{2}+\frac{2}{3}m+\frac{1}{9}=\frac{10}{9}$$

m^{2}+\frac{2}{3}m+\frac{1}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(m+\frac{1}{3}\right)^{2}=\frac{10}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m+\frac{1}{3}\right)^{2}}=\sqrt{\frac{10}{9}}$$

Qisqartirish.

$$m+\frac{1}{3}=\frac{\sqrt{10}}{3} m+\frac{1}{3}=-\frac{\sqrt{10}}{3}$$

Tenglamaning ikkala tarafidan \frac{1}{3} ni ayirish.

$$m=\frac{\sqrt{10}-1}{3} m=\frac{-\sqrt{10}-1}{3}$$