k^2-2k-35 eching

$$k ^ { 2 } - 2 k - 35$$

Omil

$$\left(k-7\right)\left(k+5\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda k^{2}+ak+bk-35 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=1\left(-35\right)=-35$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -35-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-35 5,-7$$

Har bir juftlik yigʻindisini hisoblang.

$$1-35=-34 5-7=-2$$

Yechim – -2 yigʻindisini beruvchi juftlik.

$$a=-7 b=5$$

k^{2}-2k-35 ni \left(k^{2}-7k\right)+\left(5k-35\right) sifatida qaytadan yozish.

$$\left(k^{2}-7k\right)+\left(5k-35\right)$$

Birinchi guruhda k ni va ikkinchi guruhda 5 ni faktordan chiqaring.

$$k\left(k-7\right)+5\left(k-7\right)$$

Distributiv funktsiyasidan foydalangan holda k-7 umumiy terminini chiqaring.

$$\left(k-7\right)\left(k+5\right)$$

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.

$$k^{2}-2k-35=0$$

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.

$$k=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-35\right)}}{2}$$

-2 kvadratini chiqarish.

$$k=\frac{-\left(-2\right)±\sqrt{4-4\left(-35\right)}}{2}$$

-4 ni -35 marotabaga ko'paytirish.

$$k=\frac{-\left(-2\right)±\sqrt{4+140}}{2}$$

4 ni 140 ga qo'shish.

$$k=\frac{-\left(-2\right)±\sqrt{144}}{2}$$

144 ning kvadrat ildizini chiqarish.

$$k=\frac{-\left(-2\right)±12}{2}$$

-2 ning teskarisi 2 ga teng.

$$k=\frac{2±12}{2}$$

k=\frac{2±12}{2} tenglamasini yeching, bunda ± musbat. 2 ni 12 ga qo'shish.

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

14 ni 2 ga bo'lish.

$$k=7$$

k=\frac{2±12}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 12 ni ayirish.

$$k=-\frac{10}{2}$$

-10 ni 2 ga bo'lish.

$$k=-5$$

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 -5 ga bo‘ling.

$$k^{2}-2k-35=\left(k-7\right)\left(k-\left(-5\right)\right)$$

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

$$k^{2}-2k-35=\left(k-7\right)\left(k+5\right)$$

Baholash

$$\left(k-7\right)\left(k+5\right)$$