m^2-21m-72 eching

$$m ^ { 2 } - 21 m - 72$$

Omil

$$\left(m-24\right)\left(m+3\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda m^{2}+am+bm-72 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-21 ab=1\left(-72\right)=-72$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -72-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-72 2,-36 3,-24 4,-18 6,-12 8,-9$$

Har bir juftlik yigʻindisini hisoblang.

$$1-72=-71 2-36=-34 3-24=-21 4-18=-14 6-12=-6 8-9=-1$$

Yechim – -21 yigʻindisini beruvchi juftlik.

$$a=-24 b=3$$

m^{2}-21m-72 ni \left(m^{2}-24m\right)+\left(3m-72\right) sifatida qaytadan yozish.

$$\left(m^{2}-24m\right)+\left(3m-72\right)$$

Birinchi guruhda m ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$m\left(m-24\right)+3\left(m-24\right)$$

Distributiv funktsiyasidan foydalangan holda m-24 umumiy terminini chiqaring.

$$\left(m-24\right)\left(m+3\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$m^{2}-21m-72=0$$

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.

$$m=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\left(-72\right)}}{2}$$

-21 kvadratini chiqarish.

$$m=\frac{-\left(-21\right)±\sqrt{441-4\left(-72\right)}}{2}$$

-4 ni -72 marotabaga ko'paytirish.

$$m=\frac{-\left(-21\right)±\sqrt{441+288}}{2}$$

441 ni 288 ga qo'shish.

$$m=\frac{-\left(-21\right)±\sqrt{729}}{2}$$

729 ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-21\right)±27}{2}$$

-21 ning teskarisi 21 ga teng.

$$m=\frac{21±27}{2}$$

m=\frac{21±27}{2} tenglamasini yeching, bunda ± musbat. 21 ni 27 ga qo'shish.

$$m=\frac{48}{2}$$

48 ni 2 ga bo'lish.

$$m=24$$

m=\frac{21±27}{2} tenglamasini yeching, bunda ± manfiy. 21 dan 27 ni ayirish.

$$m=-\frac{6}{2}$$

-6 ni 2 ga bo'lish.

$$m=-3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 24 ga va x_{2} uchun -3 ga bo‘ling.

$$m^{2}-21m-72=\left(m-24\right)\left(m-\left(-3\right)\right)$$

p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.

$$m^{2}-21m-72=\left(m-24\right)\left(m+3\right)$$

Baholash

$$\left(m-24\right)\left(m+3\right)$$