m^2-2m-3=1/2 eching

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

m uchun yechish

$$m=\frac{3\sqrt{2}}{2}+1\approx 3,121320344$$

$$m=-\frac{3\sqrt{2}}{2}+1\approx -1,121320344$$

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.

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

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

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

O‘zidan \frac{1}{2} ayirilsa 0 qoladi.

$$m^{2}-2m-3-\frac{1}{2}=0$$

-3 dan \frac{1}{2} ni ayirish.

$$m^{2}-2m-\frac{7}{2}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va -\frac{7}{2} ni c bilan almashtiring.

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

-2 kvadratini chiqarish.

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

-4 ni -\frac{7}{2} marotabaga ko'paytirish.

$$m=\frac{-\left(-2\right)±\sqrt{4+14}}{2}$$

4 ni 14 ga qo'shish.

$$m=\frac{-\left(-2\right)±\sqrt{18}}{2}$$

18 ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

$$m=\frac{2±3\sqrt{2}}{2}$$

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

$$m=\frac{3\sqrt{2}+2}{2}$$

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

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

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

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

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

$$m=-\frac{3\sqrt{2}}{2}+1$$

Tenglama yechildi.

$$m=\frac{3\sqrt{2}}{2}+1 m=-\frac{3\sqrt{2}}{2}+1$$

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.

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

3 ni tenglamaning ikkala tarafiga qo'shish.

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

O‘zidan -3 ayirilsa 0 qoladi.

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

\frac{1}{2} dan -3 ni ayirish.

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

-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.

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

\frac{7}{2} ni 1 ga qo'shish.

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

m^{2}-2m+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.

$$\left(m-1\right)^{2}=\frac{9}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$m-1=\frac{3\sqrt{2}}{2} m-1=-\frac{3\sqrt{2}}{2}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$m=\frac{3\sqrt{2}}{2}+1 m=-\frac{3\sqrt{2}}{2}+1$$