w^2-9w+14= eching

$$w ^ { 2 } - 9 w + 14 =$$

Omil

$$\left(w-7\right)\left(w-2\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda w^{2}+aw+bw+14 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-9 ab=1\times 14=14$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. 14-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,-14 -2,-7$$

Har bir juftlik yigʻindisini hisoblang.

$$-1-14=-15 -2-7=-9$$

Yechim – -9 yigʻindisini beruvchi juftlik.

$$a=-7 b=-2$$

w^{2}-9w+14 ni \left(w^{2}-7w\right)+\left(-2w+14\right) sifatida qaytadan yozish.

$$\left(w^{2}-7w\right)+\left(-2w+14\right)$$

Birinchi guruhda w ni va ikkinchi guruhda -2 ni faktordan chiqaring.

$$w\left(w-7\right)-2\left(w-7\right)$$

Distributiv funktsiyasidan foydalangan holda w-7 umumiy terminini chiqaring.

$$\left(w-7\right)\left(w-2\right)$$

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.

$$w^{2}-9w+14=0$$

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.

$$w=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 14}}{2}$$

-9 kvadratini chiqarish.

$$w=\frac{-\left(-9\right)±\sqrt{81-4\times 14}}{2}$$

-4 ni 14 marotabaga ko'paytirish.

$$w=\frac{-\left(-9\right)±\sqrt{81-56}}{2}$$

81 ni -56 ga qo'shish.

$$w=\frac{-\left(-9\right)±\sqrt{25}}{2}$$

25 ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-9\right)±5}{2}$$

-9 ning teskarisi 9 ga teng.

$$w=\frac{9±5}{2}$$

w=\frac{9±5}{2} tenglamasini yeching, bunda ± musbat. 9 ni 5 ga qo'shish.

$$w=\frac{14}{2}$$

14 ni 2 ga bo'lish.

$$w=7$$

w=\frac{9±5}{2} tenglamasini yeching, bunda ± manfiy. 9 dan 5 ni ayirish.

$$w=\frac{4}{2}$$

4 ni 2 ga bo'lish.

$$w=2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 7 ga va x_{2} uchun 2 ga bo‘ling.

$$w^{2}-9w+14=\left(w-7\right)\left(w-2\right)$$

Baholash

$$\left(w-7\right)\left(w-2\right)$$