m^2-6/5=m eching

$$\frac { m ^ { 2 } - 6 } { 5 } = m$$

m uchun yechish

$$m=-1$$

$$m=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

\frac{1}{5}m^{2}-\frac{6}{5} natijani olish uchun m^{2}-6 ning har bir ifodasini 5 ga bo‘ling.

$$\frac{1}{5}m^{2}-\frac{6}{5}=m$$

Ikkala tarafdan m ni ayirish.

$$\frac{1}{5}m^{2}-\frac{6}{5}-m=0$$

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.

$$\frac{1}{5}m^{2}-m-\frac{6}{5}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{5} ni a, -1 ni b va -\frac{6}{5} ni c bilan almashtiring.

$$m=\frac{-\left(-1\right)±\sqrt{1-4\times \frac{1}{5}\left(-\frac{6}{5}\right)}}{2\times \frac{1}{5}}$$

-4 ni \frac{1}{5} marotabaga ko'paytirish.

$$m=\frac{-\left(-1\right)±\sqrt{1-\frac{4}{5}\left(-\frac{6}{5}\right)}}{2\times \frac{1}{5}}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali -\frac{4}{5} ni -\frac{6}{5} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$m=\frac{-\left(-1\right)±\sqrt{1+\frac{24}{25}}}{2\times \frac{1}{5}}$$

1 ni \frac{24}{25} ga qo'shish.

$$m=\frac{-\left(-1\right)±\sqrt{\frac{49}{25}}}{2\times \frac{1}{5}}$$

\frac{49}{25} ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-1\right)±\frac{7}{5}}{2\times \frac{1}{5}}$$

-1 ning teskarisi 1 ga teng.

$$m=\frac{1±\frac{7}{5}}{2\times \frac{1}{5}}$$

2 ni \frac{1}{5} marotabaga ko'paytirish.

$$m=\frac{1±\frac{7}{5}}{\frac{2}{5}}$$

m=\frac{1±\frac{7}{5}}{\frac{2}{5}} tenglamasini yeching, bunda ± musbat. 1 ni \frac{7}{5} ga qo'shish.

$$m=\frac{\frac{12}{5}}{\frac{2}{5}}$$

\frac{12}{5} ni \frac{2}{5} ga bo'lish \frac{12}{5} ga k'paytirish \frac{2}{5} ga qaytarish.

$$m=6$$

m=\frac{1±\frac{7}{5}}{\frac{2}{5}} tenglamasini yeching, bunda ± manfiy. 1 dan \frac{7}{5} ni ayirish.

$$m=-\frac{\frac{2}{5}}{\frac{2}{5}}$$

-\frac{2}{5} ni \frac{2}{5} ga bo'lish -\frac{2}{5} ga k'paytirish \frac{2}{5} ga qaytarish.

$$m=-1$$

Tenglama yechildi.

$$m=6 m=-1$$

Kvadratni yakunlash bo'yicha qadamlar

\frac{1}{5}m^{2}-\frac{6}{5} natijani olish uchun m^{2}-6 ning har bir ifodasini 5 ga bo‘ling.

$$\frac{1}{5}m^{2}-\frac{6}{5}=m$$

Ikkala tarafdan m ni ayirish.

$$\frac{1}{5}m^{2}-\frac{6}{5}-m=0$$

\frac{6}{5} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{1}{5}m^{2}-m=\frac{6}{5}$$

Ikkala tarafini 5 ga ko‘paytiring.

$$\frac{\frac{1}{5}m^{2}-m}{\frac{1}{5}}=\frac{\frac{6}{5}}{\frac{1}{5}}$$

\frac{1}{5} ga bo'lish \frac{1}{5} ga ko'paytirishni bekor qiladi.

$$m^{2}+\left(-\frac{1}{\frac{1}{5}}\right)m=\frac{\frac{6}{5}}{\frac{1}{5}}$$

-1 ni \frac{1}{5} ga bo'lish -1 ga k'paytirish \frac{1}{5} ga qaytarish.

$$m^{2}-5m=\frac{\frac{6}{5}}{\frac{1}{5}}$$

\frac{6}{5} ni \frac{1}{5} ga bo'lish \frac{6}{5} ga k'paytirish \frac{1}{5} ga qaytarish.

$$m^{2}-5m=6$$

-5 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{2} olish uchun. Keyin, -\frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}-5m+\left(-\frac{5}{2}\right)^{2}=6+\left(-\frac{5}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{2} kvadratini chiqarish.

$$m^{2}-5m+\frac{25}{4}=6+\frac{25}{4}$$

6 ni \frac{25}{4} ga qo'shish.

$$m^{2}-5m+\frac{25}{4}=\frac{49}{4}$$

m^{2}-5m+\frac{25}{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.

$$\left(m-\frac{5}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-\frac{5}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$m-\frac{5}{2}=\frac{7}{2} m-\frac{5}{2}=-\frac{7}{2}$$

\frac{5}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$m=6 m=-1$$