m+2=m^2+2m-3 eching

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

m uchun yechish

$$m = \frac{\sqrt{21} - 1}{2} \approx 1,791287847$$

$$m=\frac{-\sqrt{21}-1}{2}\approx -2,791287847$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan m^{2} ni ayirish.

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

Ikkala tarafdan 2m ni ayirish.

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

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

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

3 ni ikki tarafga qo’shing.

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

5 olish uchun 2 va 3'ni qo'shing.

$$-m+5-m^{2}=0$$

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.

$$-m^{2}-m+5=0$$

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

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

-4 ni -1 marotabaga ko'paytirish.

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

4 ni 5 marotabaga ko'paytirish.

$$m=\frac{-\left(-1\right)±\sqrt{1+20}}{2\left(-1\right)}$$

1 ni 20 ga qo'shish.

$$m=\frac{-\left(-1\right)±\sqrt{21}}{2\left(-1\right)}$$

-1 ning teskarisi 1 ga teng.

$$m=\frac{1±\sqrt{21}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$m=\frac{1±\sqrt{21}}{-2}$$

m=\frac{1±\sqrt{21}}{-2} tenglamasini yeching, bunda ± musbat. 1 ni \sqrt{21} ga qo'shish.

$$m=\frac{\sqrt{21}+1}{-2}$$

1+\sqrt{21} ni -2 ga bo'lish.

$$m=\frac{-\sqrt{21}-1}{2}$$

m=\frac{1±\sqrt{21}}{-2} tenglamasini yeching, bunda ± manfiy. 1 dan \sqrt{21} ni ayirish.

$$m=\frac{1-\sqrt{21}}{-2}$$

1-\sqrt{21} ni -2 ga bo'lish.

$$m=\frac{\sqrt{21}-1}{2}$$

Tenglama yechildi.

$$m=\frac{-\sqrt{21}-1}{2} m=\frac{\sqrt{21}-1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan m^{2} ni ayirish.

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

Ikkala tarafdan 2m ni ayirish.

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

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

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

Ikkala tarafdan 2 ni ayirish.

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

-5 olish uchun -3 dan 2 ni ayirish.

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

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

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

Ikki tarafini -1 ga bo‘ling.

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

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

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

-1 ni -1 ga bo'lish.

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

-5 ni -1 ga bo'lish.

$$m^{2}+m=5$$

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.

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

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

$$m^{2}+m+\frac{1}{4}=5+\frac{1}{4}$$

5 ni \frac{1}{4} ga qo'shish.

$$m^{2}+m+\frac{1}{4}=\frac{21}{4}$$

m^{2}+m+\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.

$$\left(m+\frac{1}{2}\right)^{2}=\frac{21}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m+\frac{1}{2}\right)^{2}}=\sqrt{\frac{21}{4}}$$

Qisqartirish.

$$m+\frac{1}{2}=\frac{\sqrt{21}}{2} m+\frac{1}{2}=-\frac{\sqrt{21}}{2}$$

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

$$m=\frac{\sqrt{21}-1}{2} m=\frac{-\sqrt{21}-1}{2}$$