m^2-13m+72=0 eching

$${ m }^{ 2 } -13m+72=0$$

m uchun yechish

$$m=\frac{13+\sqrt{119}i}{2}\approx 6,5+5,454356057i$$

$$m=\frac{-\sqrt{119}i+13}{2}\approx 6,5-5,454356057i$$

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.

$$m^{2}-13m+72=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -13 ni b va 72 ni c bilan almashtiring.

$$m=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 72}}{2}$$

-13 kvadratini chiqarish.

$$m=\frac{-\left(-13\right)±\sqrt{169-4\times 72}}{2}$$

-4 ni 72 marotabaga ko'paytirish.

$$m=\frac{-\left(-13\right)±\sqrt{169-288}}{2}$$

169 ni -288 ga qo'shish.

$$m=\frac{-\left(-13\right)±\sqrt{-119}}{2}$$

-119 ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-13\right)±\sqrt{119}i}{2}$$

-13 ning teskarisi 13 ga teng.

$$m=\frac{13±\sqrt{119}i}{2}$$

m=\frac{13±\sqrt{119}i}{2} tenglamasini yeching, bunda ± musbat. 13 ni i\sqrt{119} ga qo'shish.

$$m=\frac{13+\sqrt{119}i}{2}$$

m=\frac{13±\sqrt{119}i}{2} tenglamasini yeching, bunda ± manfiy. 13 dan i\sqrt{119} ni ayirish.

$$m=\frac{-\sqrt{119}i+13}{2}$$

Tenglama yechildi.

$$m=\frac{13+\sqrt{119}i}{2} m=\frac{-\sqrt{119}i+13}{2}$$

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.

$$m^{2}-13m+72=0$$

Tenglamaning ikkala tarafidan 72 ni ayirish.

$$m^{2}-13m+72-72=-72$$

O‘zidan 72 ayirilsa 0 qoladi.

$$m^{2}-13m=-72$$

-13 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{13}{2} olish uchun. Keyin, -\frac{13}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}-13m+\left(-\frac{13}{2}\right)^{2}=-72+\left(-\frac{13}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{13}{2} kvadratini chiqarish.

$$m^{2}-13m+\frac{169}{4}=-72+\frac{169}{4}$$

-72 ni \frac{169}{4} ga qo'shish.

$$m^{2}-13m+\frac{169}{4}=-\frac{119}{4}$$

m^{2}-13m+\frac{169}{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.

$$\left(m-\frac{13}{2}\right)^{2}=-\frac{119}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-\frac{13}{2}\right)^{2}}=\sqrt{-\frac{119}{4}}$$

Qisqartirish.

$$m-\frac{13}{2}=\frac{\sqrt{119}i}{2} m-\frac{13}{2}=-\frac{\sqrt{119}i}{2}$$

\frac{13}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$m=\frac{13+\sqrt{119}i}{2} m=\frac{-\sqrt{119}i+13}{2}$$