p+2=p+2/p-3 eching

$$p + 2 = \frac { p + 2 } { p - 3 }$$

p uchun yechish

$$p=-2$$

$$p=4$$

Kvadrat tenglamalaridan foydalanish qoidalari

p qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini p-3 ga ko'paytirish.

$$\left(p-3\right)p+\left(p-3\right)\times 2=p+2$$

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

$$p^{2}-3p+\left(p-3\right)\times 2=p+2$$

p-3 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$p^{2}-3p+2p-6=p+2$$

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

$$p^{2}-p-6=p+2$$

Ikkala tarafdan p ni ayirish.

$$p^{2}-p-6-p=2$$

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

$$p^{2}-2p-6=2$$

Ikkala tarafdan 2 ni ayirish.

$$p^{2}-2p-6-2=0$$

-8 olish uchun -6 dan 2 ni ayirish.

$$p^{2}-2p-8=0$$

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 -8 ni c bilan almashtiring.

$$p=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-8\right)}}{2}$$

-2 kvadratini chiqarish.

$$p=\frac{-\left(-2\right)±\sqrt{4-4\left(-8\right)}}{2}$$

-4 ni -8 marotabaga ko'paytirish.

$$p=\frac{-\left(-2\right)±\sqrt{4+32}}{2}$$

4 ni 32 ga qo'shish.

$$p=\frac{-\left(-2\right)±\sqrt{36}}{2}$$

36 ning kvadrat ildizini chiqarish.

$$p=\frac{-\left(-2\right)±6}{2}$$

-2 ning teskarisi 2 ga teng.

$$p=\frac{2±6}{2}$$

p=\frac{2±6}{2} tenglamasini yeching, bunda ± musbat. 2 ni 6 ga qo'shish.

$$p=\frac{8}{2}$$

8 ni 2 ga bo'lish.

$$p=4$$

p=\frac{2±6}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 6 ni ayirish.

$$p=-\frac{4}{2}$$

-4 ni 2 ga bo'lish.

$$p=-2$$

Tenglama yechildi.

$$p=4 p=-2$$

Kvadratni yakunlash bo'yicha qadamlar

p qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini p-3 ga ko'paytirish.

$$\left(p-3\right)p+\left(p-3\right)\times 2=p+2$$

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

$$p^{2}-3p+\left(p-3\right)\times 2=p+2$$

p-3 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$p^{2}-3p+2p-6=p+2$$

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

$$p^{2}-p-6=p+2$$

Ikkala tarafdan p ni ayirish.

$$p^{2}-p-6-p=2$$

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

$$p^{2}-2p-6=2$$

6 ni ikki tarafga qo’shing.

$$p^{2}-2p=2+6$$

8 olish uchun 2 va 6'ni qo'shing.

$$p^{2}-2p=8$$

-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.

$$p^{2}-2p+1=8+1$$

8 ni 1 ga qo'shish.

$$p^{2}-2p+1=9$$

p^{2}-2p+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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$p-1=3 p-1=-3$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$p=4 p=-2$$