4u^2-12u-16 eching

$$4 u ^ { 2 } - 12 u - 16$$

Omil

$$4\left(u-4\right)\left(u+1\right)$$

Yechim qadamlari

4 omili.

$$4\left(u^{2}-3u-4\right)$$

Hisoblang: u^{2}-3u-4. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda u^{2}+au+bu-4 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-3 ab=1\left(-4\right)=-4$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -4-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-4 2,-2$$

Har bir juftlik yigʻindisini hisoblang.

$$1-4=-3 2-2=0$$

Yechim – -3 yigʻindisini beruvchi juftlik.

$$a=-4 b=1$$

u^{2}-3u-4 ni \left(u^{2}-4u\right)+\left(u-4\right) sifatida qaytadan yozish.

$$\left(u^{2}-4u\right)+\left(u-4\right)$$

u^{2}-4u ichida u ni ajrating.

$$u\left(u-4\right)+u-4$$

Distributiv funktsiyasidan foydalangan holda u-4 umumiy terminini chiqaring.

$$\left(u-4\right)\left(u+1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$4\left(u-4\right)\left(u+1\right)$$

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.

$$4u^{2}-12u-16=0$$

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.

$$u=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 4\left(-16\right)}}{2\times 4}$$

-12 kvadratini chiqarish.

$$u=\frac{-\left(-12\right)±\sqrt{144-4\times 4\left(-16\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$u=\frac{-\left(-12\right)±\sqrt{144-16\left(-16\right)}}{2\times 4}$$

-16 ni -16 marotabaga ko'paytirish.

$$u=\frac{-\left(-12\right)±\sqrt{144+256}}{2\times 4}$$

144 ni 256 ga qo'shish.

$$u=\frac{-\left(-12\right)±\sqrt{400}}{2\times 4}$$

400 ning kvadrat ildizini chiqarish.

$$u=\frac{-\left(-12\right)±20}{2\times 4}$$

-12 ning teskarisi 12 ga teng.

$$u=\frac{12±20}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$u=\frac{12±20}{8}$$

u=\frac{12±20}{8} tenglamasini yeching, bunda ± musbat. 12 ni 20 ga qo'shish.

$$u=\frac{32}{8}$$

32 ni 8 ga bo'lish.

$$u=4$$

u=\frac{12±20}{8} tenglamasini yeching, bunda ± manfiy. 12 dan 20 ni ayirish.

$$u=-\frac{8}{8}$$

-8 ni 8 ga bo'lish.

$$u=-1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 4 ga va x_{2} uchun -1 ga bo‘ling.

$$4u^{2}-12u-16=4\left(u-4\right)\left(u-\left(-1\right)\right)$$

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

$$4u^{2}-12u-16=4\left(u-4\right)\left(u+1\right)$$

Baholash

$$4\left(u-4\right)\left(u+1\right)$$