4m^2-36m+26=0 eching

$$4 m ^ { 2 } - 36 m + 26 = 0$$

m uchun yechish

$$m = \frac{\sqrt{55} + 9}{2} \approx 8,208099244$$

$$m=\frac{9-\sqrt{55}}{2}\approx 0,791900756$$

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.

$$4m^{2}-36m+26=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -36 ni b va 26 ni c bilan almashtiring.

$$m=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 4\times 26}}{2\times 4}$$

-36 kvadratini chiqarish.

$$m=\frac{-\left(-36\right)±\sqrt{1296-4\times 4\times 26}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$m=\frac{-\left(-36\right)±\sqrt{1296-16\times 26}}{2\times 4}$$

-16 ni 26 marotabaga ko'paytirish.

$$m=\frac{-\left(-36\right)±\sqrt{1296-416}}{2\times 4}$$

1296 ni -416 ga qo'shish.

$$m=\frac{-\left(-36\right)±\sqrt{880}}{2\times 4}$$

880 ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-36\right)±4\sqrt{55}}{2\times 4}$$

-36 ning teskarisi 36 ga teng.

$$m=\frac{36±4\sqrt{55}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$m=\frac{36±4\sqrt{55}}{8}$$

m=\frac{36±4\sqrt{55}}{8} tenglamasini yeching, bunda ± musbat. 36 ni 4\sqrt{55} ga qo'shish.

$$m=\frac{4\sqrt{55}+36}{8}$$

36+4\sqrt{55} ni 8 ga bo'lish.

$$m=\frac{\sqrt{55}+9}{2}$$

m=\frac{36±4\sqrt{55}}{8} tenglamasini yeching, bunda ± manfiy. 36 dan 4\sqrt{55} ni ayirish.

$$m=\frac{36-4\sqrt{55}}{8}$$

36-4\sqrt{55} ni 8 ga bo'lish.

$$m=\frac{9-\sqrt{55}}{2}$$

Tenglama yechildi.

$$m=\frac{\sqrt{55}+9}{2} m=\frac{9-\sqrt{55}}{2}$$

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.

$$4m^{2}-36m+26=0$$

Tenglamaning ikkala tarafidan 26 ni ayirish.

$$4m^{2}-36m+26-26=-26$$

O‘zidan 26 ayirilsa 0 qoladi.

$$4m^{2}-36m=-26$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4m^{2}-36m}{4}=-\frac{26}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$m^{2}+\left(-\frac{36}{4}\right)m=-\frac{26}{4}$$

-36 ni 4 ga bo'lish.

$$m^{2}-9m=-\frac{26}{4}$$

\frac{-26}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$m^{2}-9m=-\frac{13}{2}$$

-9 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{2} olish uchun. Keyin, -\frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}-9m+\left(-\frac{9}{2}\right)^{2}=-\frac{13}{2}+\left(-\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{2} kvadratini chiqarish.

$$m^{2}-9m+\frac{81}{4}=-\frac{13}{2}+\frac{81}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{13}{2} ni \frac{81}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$m^{2}-9m+\frac{81}{4}=\frac{55}{4}$$

m^{2}-9m+\frac{81}{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.

$$\left(m-\frac{9}{2}\right)^{2}=\frac{55}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-\frac{9}{2}\right)^{2}}=\sqrt{\frac{55}{4}}$$

Qisqartirish.

$$m-\frac{9}{2}=\frac{\sqrt{55}}{2} m-\frac{9}{2}=-\frac{\sqrt{55}}{2}$$

\frac{9}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$m=\frac{\sqrt{55}+9}{2} m=\frac{9-\sqrt{55}}{2}$$