3d^2-51d+126 eching

$$3 { d }^{ 2 } -51d+126$$

Omil

$$3\left(d-14\right)\left(d-3\right)$$

Yechim qadamlari

3 omili.

$$3\left(d^{2}-17d+42\right)$$

Hisoblang: d^{2}-17d+42. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda d^{2}+ad+bd+42 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-17 ab=1\times 42=42$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. 42-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,-42 -2,-21 -3,-14 -6,-7$$

Har bir juftlik yigʻindisini hisoblang.

$$-1-42=-43 -2-21=-23 -3-14=-17 -6-7=-13$$

Yechim – -17 yigʻindisini beruvchi juftlik.

$$a=-14 b=-3$$

d^{2}-17d+42 ni \left(d^{2}-14d\right)+\left(-3d+42\right) sifatida qaytadan yozish.

$$\left(d^{2}-14d\right)+\left(-3d+42\right)$$

Birinchi guruhda d ni va ikkinchi guruhda -3 ni faktordan chiqaring.

$$d\left(d-14\right)-3\left(d-14\right)$$

Distributiv funktsiyasidan foydalangan holda d-14 umumiy terminini chiqaring.

$$\left(d-14\right)\left(d-3\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$3\left(d-14\right)\left(d-3\right)$$

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.

$$3d^{2}-51d+126=0$$

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.

$$d=\frac{-\left(-51\right)±\sqrt{\left(-51\right)^{2}-4\times 3\times 126}}{2\times 3}$$

-51 kvadratini chiqarish.

$$d=\frac{-\left(-51\right)±\sqrt{2601-4\times 3\times 126}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$d=\frac{-\left(-51\right)±\sqrt{2601-12\times 126}}{2\times 3}$$

-12 ni 126 marotabaga ko'paytirish.

$$d=\frac{-\left(-51\right)±\sqrt{2601-1512}}{2\times 3}$$

2601 ni -1512 ga qo'shish.

$$d=\frac{-\left(-51\right)±\sqrt{1089}}{2\times 3}$$

1089 ning kvadrat ildizini chiqarish.

$$d=\frac{-\left(-51\right)±33}{2\times 3}$$

-51 ning teskarisi 51 ga teng.

$$d=\frac{51±33}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$d=\frac{51±33}{6}$$

d=\frac{51±33}{6} tenglamasini yeching, bunda ± musbat. 51 ni 33 ga qo'shish.

$$d=\frac{84}{6}$$

84 ni 6 ga bo'lish.

$$d=14$$

d=\frac{51±33}{6} tenglamasini yeching, bunda ± manfiy. 51 dan 33 ni ayirish.

$$d=\frac{18}{6}$$

18 ni 6 ga bo'lish.

$$d=3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 14 ga va x_{2} uchun 3 ga bo‘ling.

$$3d^{2}-51d+126=3\left(d-14\right)\left(d-3\right)$$

Baholash

$$3\left(d-14\right)\left(d-3\right)$$