24x^2-72x+48 eching

$$24 x ^ { 2 } - 72 x + 48$$

Omil

$$24\left(x-2\right)\left(x-1\right)$$

Yechim qadamlari

24 omili.

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

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

$$a+b=-3 ab=1\times 2=2$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. Faqat bundan juftlik tizim yechimidir.

$$a=-2 b=-1$$

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

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

Birinchi guruhda x ni va ikkinchi guruhda -1 ni faktordan chiqaring.

$$x\left(x-2\right)-\left(x-2\right)$$

Distributiv funktsiyasidan foydalangan holda x-2 umumiy terminini chiqaring.

$$\left(x-2\right)\left(x-1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$24\left(x-2\right)\left(x-1\right)$$

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.

$$24x^{2}-72x+48=0$$

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.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\times 24\times 48}}{2\times 24}$$

-72 kvadratini chiqarish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4\times 24\times 48}}{2\times 24}$$

-4 ni 24 marotabaga ko'paytirish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-96\times 48}}{2\times 24}$$

-96 ni 48 marotabaga ko'paytirish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4608}}{2\times 24}$$

5184 ni -4608 ga qo'shish.

$$x=\frac{-\left(-72\right)±\sqrt{576}}{2\times 24}$$

576 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-72\right)±24}{2\times 24}$$

-72 ning teskarisi 72 ga teng.

$$x=\frac{72±24}{2\times 24}$$

2 ni 24 marotabaga ko'paytirish.

$$x=\frac{72±24}{48}$$

x=\frac{72±24}{48} tenglamasini yeching, bunda ± musbat. 72 ni 24 ga qo'shish.

$$x=\frac{96}{48}$$

96 ni 48 ga bo'lish.

$$x=2$$

x=\frac{72±24}{48} tenglamasini yeching, bunda ± manfiy. 72 dan 24 ni ayirish.

$$x=\frac{48}{48}$$

48 ni 48 ga bo'lish.

$$x=1$$

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

$$24x^{2}-72x+48=24\left(x-2\right)\left(x-1\right)$$

Baholash

$$24\left(x-2\right)\left(x-1\right)$$