k^2-3k-180 eching

$$k ^ { 2 } - 3 k - 180$$

Omil

$$\left(k-15\right)\left(k+12\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda k^{2}+ak+bk-180 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-3 ab=1\left(-180\right)=-180$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -180-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-180 2,-90 3,-60 4,-45 5,-36 6,-30 9,-20 10,-18 12,-15$$

Har bir juftlik yigʻindisini hisoblang.

$$1-180=-179 2-90=-88 3-60=-57 4-45=-41 5-36=-31 6-30=-24 9-20=-11 10-18=-8 12-15=-3$$

Yechim – -3 yigʻindisini beruvchi juftlik.

$$a=-15 b=12$$

k^{2}-3k-180 ni \left(k^{2}-15k\right)+\left(12k-180\right) sifatida qaytadan yozish.

$$\left(k^{2}-15k\right)+\left(12k-180\right)$$

Birinchi guruhda k ni va ikkinchi guruhda 12 ni faktordan chiqaring.

$$k\left(k-15\right)+12\left(k-15\right)$$

Distributiv funktsiyasidan foydalangan holda k-15 umumiy terminini chiqaring.

$$\left(k-15\right)\left(k+12\right)$$

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.

$$k^{2}-3k-180=0$$

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.

$$k=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-180\right)}}{2}$$

-3 kvadratini chiqarish.

$$k=\frac{-\left(-3\right)±\sqrt{9-4\left(-180\right)}}{2}$$

-4 ni -180 marotabaga ko'paytirish.

$$k=\frac{-\left(-3\right)±\sqrt{9+720}}{2}$$

9 ni 720 ga qo'shish.

$$k=\frac{-\left(-3\right)±\sqrt{729}}{2}$$

729 ning kvadrat ildizini chiqarish.

$$k=\frac{-\left(-3\right)±27}{2}$$

-3 ning teskarisi 3 ga teng.

$$k=\frac{3±27}{2}$$

k=\frac{3±27}{2} tenglamasini yeching, bunda ± musbat. 3 ni 27 ga qo'shish.

$$k=\frac{30}{2}$$

30 ni 2 ga bo'lish.

$$k=15$$

k=\frac{3±27}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 27 ni ayirish.

$$k=-\frac{24}{2}$$

-24 ni 2 ga bo'lish.

$$k=-12$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 15 ga va x_{2} uchun -12 ga bo‘ling.

$$k^{2}-3k-180=\left(k-15\right)\left(k-\left(-12\right)\right)$$

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

$$k^{2}-3k-180=\left(k-15\right)\left(k+12\right)$$

Baholash

$$\left(k-15\right)\left(k+12\right)$$