31p^2-37p=0 eching

$$31 p ^ { 2 } - 37 p = 0$$

p uchun yechish

$$p = \frac{37}{31} = 1\frac{6}{31} \approx 1,193548387$$

$$p=0$$

Faktorlash qadamlari

p omili.

$$p\left(31p-37\right)=0$$

Tenglamani yechish uchun p=0 va 31p-37=0 ni yeching.

$$p=0 p=\frac{37}{31}$$

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.

$$31p^{2}-37p=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 31 ni a, -37 ni b va 0 ni c bilan almashtiring.

$$p=\frac{-\left(-37\right)±\sqrt{\left(-37\right)^{2}}}{2\times 31}$$

\left(-37\right)^{2} ning kvadrat ildizini chiqarish.

$$p=\frac{-\left(-37\right)±37}{2\times 31}$$

-37 ning teskarisi 37 ga teng.

$$p=\frac{37±37}{2\times 31}$$

2 ni 31 marotabaga ko'paytirish.

$$p=\frac{37±37}{62}$$

p=\frac{37±37}{62} tenglamasini yeching, bunda ± musbat. 37 ni 37 ga qo'shish.

$$p=\frac{74}{62}$$

\frac{74}{62} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$p=\frac{37}{31}$$

p=\frac{37±37}{62} tenglamasini yeching, bunda ± manfiy. 37 dan 37 ni ayirish.

$$p=\frac{0}{62}$$

0 ni 62 ga bo'lish.

$$p=0$$

Tenglama yechildi.

$$p=\frac{37}{31} p=0$$

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.

$$31p^{2}-37p=0$$

Ikki tarafini 31 ga bo‘ling.

$$\frac{31p^{2}-37p}{31}=\frac{0}{31}$$

31 ga bo'lish 31 ga ko'paytirishni bekor qiladi.

$$p^{2}-\frac{37}{31}p=\frac{0}{31}$$

0 ni 31 ga bo'lish.

$$p^{2}-\frac{37}{31}p=0$$

-\frac{37}{31} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{37}{62} olish uchun. Keyin, -\frac{37}{62} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$p^{2}-\frac{37}{31}p+\left(-\frac{37}{62}\right)^{2}=\left(-\frac{37}{62}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{37}{62} kvadratini chiqarish.

$$p^{2}-\frac{37}{31}p+\frac{1369}{3844}=\frac{1369}{3844}$$

p^{2}-\frac{37}{31}p+\frac{1369}{3844} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(p-\frac{37}{62}\right)^{2}=\frac{1369}{3844}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(p-\frac{37}{62}\right)^{2}}=\sqrt{\frac{1369}{3844}}$$

Qisqartirish.

$$p-\frac{37}{62}=\frac{37}{62} p-\frac{37}{62}=-\frac{37}{62}$$

\frac{37}{62} ni tenglamaning ikkala tarafiga qo'shish.

$$p=\frac{37}{31} p=0$$