p^2-3p+3=175 eching

$${ p }^{ 2 } -3p+3=175$$

p uchun yechish

$$p = \frac{\sqrt{697} + 3}{2} \approx 14,700378782$$

$$p=\frac{3-\sqrt{697}}{2}\approx -11,700378782$$

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.

$$p^{2}-3p+3=175$$

Tenglamaning ikkala tarafidan 175 ni ayirish.

$$p^{2}-3p+3-175=175-175$$

O‘zidan 175 ayirilsa 0 qoladi.

$$p^{2}-3p+3-175=0$$

3 dan 175 ni ayirish.

$$p^{2}-3p-172=0$$

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 -172 ni c bilan almashtiring.

$$p=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-172\right)}}{2}$$

-3 kvadratini chiqarish.

$$p=\frac{-\left(-3\right)±\sqrt{9-4\left(-172\right)}}{2}$$

-4 ni -172 marotabaga ko'paytirish.

$$p=\frac{-\left(-3\right)±\sqrt{9+688}}{2}$$

9 ni 688 ga qo'shish.

$$p=\frac{-\left(-3\right)±\sqrt{697}}{2}$$

-3 ning teskarisi 3 ga teng.

$$p=\frac{3±\sqrt{697}}{2}$$

p=\frac{3±\sqrt{697}}{2} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{697} ga qo'shish.

$$p=\frac{\sqrt{697}+3}{2}$$

p=\frac{3±\sqrt{697}}{2} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{697} ni ayirish.

$$p=\frac{3-\sqrt{697}}{2}$$

Tenglama yechildi.

$$p=\frac{\sqrt{697}+3}{2} p=\frac{3-\sqrt{697}}{2}$$

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.

$$p^{2}-3p+3=175$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$p^{2}-3p+3-3=175-3$$

O‘zidan 3 ayirilsa 0 qoladi.

$$p^{2}-3p=175-3$$

175 dan 3 ni ayirish.

$$p^{2}-3p=172$$

-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.

$$p^{2}-3p+\left(-\frac{3}{2}\right)^{2}=172+\left(-\frac{3}{2}\right)^{2}$$

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

$$p^{2}-3p+\frac{9}{4}=172+\frac{9}{4}$$

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

$$p^{2}-3p+\frac{9}{4}=\frac{697}{4}$$

p^{2}-3p+\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.

$$\left(p-\frac{3}{2}\right)^{2}=\frac{697}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(p-\frac{3}{2}\right)^{2}}=\sqrt{\frac{697}{4}}$$

Qisqartirish.

$$p-\frac{3}{2}=\frac{\sqrt{697}}{2} p-\frac{3}{2}=-\frac{\sqrt{697}}{2}$$

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

$$p=\frac{\sqrt{697}+3}{2} p=\frac{3-\sqrt{697}}{2}$$