21m^2+21m-42 eching

$$21 m ^ { 2 } + 21 m - 42$$

Omil

$$21\left(m-1\right)\left(m+2\right)$$

Yechim qadamlari

21 omili.

$$21\left(m^{2}+m-2\right)$$

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

$$a+b=1 ab=1\left(-2\right)=-2$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

$$a=-1 b=2$$

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

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

Birinchi guruhda m ni va ikkinchi guruhda 2 ni faktordan chiqaring.

$$m\left(m-1\right)+2\left(m-1\right)$$

Distributiv funktsiyasidan foydalangan holda m-1 umumiy terminini chiqaring.

$$\left(m-1\right)\left(m+2\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$21\left(m-1\right)\left(m+2\right)$$

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.

$$21m^{2}+21m-42=0$$

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.

$$m=\frac{-21±\sqrt{21^{2}-4\times 21\left(-42\right)}}{2\times 21}$$

21 kvadratini chiqarish.

$$m=\frac{-21±\sqrt{441-4\times 21\left(-42\right)}}{2\times 21}$$

-4 ni 21 marotabaga ko'paytirish.

$$m=\frac{-21±\sqrt{441-84\left(-42\right)}}{2\times 21}$$

-84 ni -42 marotabaga ko'paytirish.

$$m=\frac{-21±\sqrt{441+3528}}{2\times 21}$$

441 ni 3528 ga qo'shish.

$$m=\frac{-21±\sqrt{3969}}{2\times 21}$$

3969 ning kvadrat ildizini chiqarish.

$$m=\frac{-21±63}{2\times 21}$$

2 ni 21 marotabaga ko'paytirish.

$$m=\frac{-21±63}{42}$$

m=\frac{-21±63}{42} tenglamasini yeching, bunda ± musbat. -21 ni 63 ga qo'shish.

$$m=\frac{42}{42}$$

42 ni 42 ga bo'lish.

$$m=1$$

m=\frac{-21±63}{42} tenglamasini yeching, bunda ± manfiy. -21 dan 63 ni ayirish.

$$m=-\frac{84}{42}$$

-84 ni 42 ga bo'lish.

$$m=-2$$

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

$$21m^{2}+21m-42=21\left(m-1\right)\left(m-\left(-2\right)\right)$$

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

$$21m^{2}+21m-42=21\left(m-1\right)\left(m+2\right)$$

Baholash

$$21\left(m-1\right)\left(m+2\right)$$