4u^2-24u-64 eching

$$4 u ^ { 2 } - 24 u - 64$$

Omil

$$4\left(u-8\right)\left(u+2\right)$$

Yechim qadamlari

4 omili.

$$4\left(u^{2}-6u-16\right)$$

Hisoblang: u^{2}-6u-16. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda u^{2}+au+bu-16 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-6 ab=1\left(-16\right)=-16$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -16-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-16 2,-8 4,-4$$

Har bir juftlik yigʻindisini hisoblang.

$$1-16=-15 2-8=-6 4-4=0$$

Yechim – -6 yigʻindisini beruvchi juftlik.

$$a=-8 b=2$$

u^{2}-6u-16 ni \left(u^{2}-8u\right)+\left(2u-16\right) sifatida qaytadan yozish.

$$\left(u^{2}-8u\right)+\left(2u-16\right)$$

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

$$u\left(u-8\right)+2\left(u-8\right)$$

Distributiv funktsiyasidan foydalangan holda u-8 umumiy terminini chiqaring.

$$\left(u-8\right)\left(u+2\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$4\left(u-8\right)\left(u+2\right)$$

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.

$$4u^{2}-24u-64=0$$

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.

$$u=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 4\left(-64\right)}}{2\times 4}$$

-24 kvadratini chiqarish.

$$u=\frac{-\left(-24\right)±\sqrt{576-4\times 4\left(-64\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$u=\frac{-\left(-24\right)±\sqrt{576-16\left(-64\right)}}{2\times 4}$$

-16 ni -64 marotabaga ko'paytirish.

$$u=\frac{-\left(-24\right)±\sqrt{576+1024}}{2\times 4}$$

576 ni 1024 ga qo'shish.

$$u=\frac{-\left(-24\right)±\sqrt{1600}}{2\times 4}$$

1600 ning kvadrat ildizini chiqarish.

$$u=\frac{-\left(-24\right)±40}{2\times 4}$$

-24 ning teskarisi 24 ga teng.

$$u=\frac{24±40}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$u=\frac{24±40}{8}$$

u=\frac{24±40}{8} tenglamasini yeching, bunda ± musbat. 24 ni 40 ga qo'shish.

$$u=\frac{64}{8}$$

64 ni 8 ga bo'lish.

$$u=8$$

u=\frac{24±40}{8} tenglamasini yeching, bunda ± manfiy. 24 dan 40 ni ayirish.

$$u=-\frac{16}{8}$$

-16 ni 8 ga bo'lish.

$$u=-2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 8 ga va x_{2} uchun -2 ga bo‘ling.

$$4u^{2}-24u-64=4\left(u-8\right)\left(u-\left(-2\right)\right)$$

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

$$4u^{2}-24u-64=4\left(u-8\right)\left(u+2\right)$$

Baholash

$$4\left(u-8\right)\left(u+2\right)$$