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

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

m uchun yechish

$$m = \frac{\sqrt{17} + 3}{2} \approx 3,561552813$$

$$m=\frac{3-\sqrt{17}}{2}\approx -0,561552813$$

Kvadrat tenglamalaridan foydalanish qoidalari

m qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini m-1 ga ko'paytirish.

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

m-3 ga m+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

Ikkala tarafdan m ni ayirish.

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

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

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

1 ni ikki tarafga qo’shing.

$$m^{2}-3m-3+1=0$$

-2 olish uchun -3 va 1'ni qo'shing.

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

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

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

-3 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

$$m=\frac{-\left(-3\right)±\sqrt{9+8}}{2}$$

9 ni 8 ga qo'shish.

$$m=\frac{-\left(-3\right)±\sqrt{17}}{2}$$

-3 ning teskarisi 3 ga teng.

$$m=\frac{3±\sqrt{17}}{2}$$

m=\frac{3±\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{17} ga qo'shish.

$$m=\frac{\sqrt{17}+3}{2}$$

m=\frac{3±\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{17} ni ayirish.

$$m=\frac{3-\sqrt{17}}{2}$$

Tenglama yechildi.

$$m=\frac{\sqrt{17}+3}{2} m=\frac{3-\sqrt{17}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

m qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini m-1 ga ko'paytirish.

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

m-3 ga m+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

Ikkala tarafdan m ni ayirish.

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

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

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

3 ni ikki tarafga qo’shing.

$$m^{2}-3m=-1+3$$

2 olish uchun -1 va 3'ni qo'shing.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$m^{2}-3m+\frac{9}{4}=2+\frac{9}{4}$$

2 ni \frac{9}{4} ga qo'shish.

$$m^{2}-3m+\frac{9}{4}=\frac{17}{4}$$

m^{2}-3m+\frac{9}{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.

$$\left(m-\frac{3}{2}\right)^{2}=\frac{17}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-\frac{3}{2}\right)^{2}}=\sqrt{\frac{17}{4}}$$

Qisqartirish.

$$m-\frac{3}{2}=\frac{\sqrt{17}}{2} m-\frac{3}{2}=-\frac{\sqrt{17}}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$m=\frac{\sqrt{17}+3}{2} m=\frac{3-\sqrt{17}}{2}$$