d^2-4d-5 eching

$$d ^ { 2 } - 4 d - 5$$

Omil

$$\left(d-5\right)\left(d+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda d^{2}+ad+bd-5 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-4 ab=1\left(-5\right)=-5$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

$$a=-5 b=1$$

d^{2}-4d-5 ni \left(d^{2}-5d\right)+\left(d-5\right) sifatida qaytadan yozish.

$$\left(d^{2}-5d\right)+\left(d-5\right)$$

d^{2}-5d ichida d ni ajrating.

$$d\left(d-5\right)+d-5$$

Distributiv funktsiyasidan foydalangan holda d-5 umumiy terminini chiqaring.

$$\left(d-5\right)\left(d+1\right)$$

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.

$$d^{2}-4d-5=0$$

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.

$$d=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-5\right)}}{2}$$

-4 kvadratini chiqarish.

$$d=\frac{-\left(-4\right)±\sqrt{16-4\left(-5\right)}}{2}$$

-4 ni -5 marotabaga ko'paytirish.

$$d=\frac{-\left(-4\right)±\sqrt{16+20}}{2}$$

16 ni 20 ga qo'shish.

$$d=\frac{-\left(-4\right)±\sqrt{36}}{2}$$

36 ning kvadrat ildizini chiqarish.

$$d=\frac{-\left(-4\right)±6}{2}$$

-4 ning teskarisi 4 ga teng.

$$d=\frac{4±6}{2}$$

d=\frac{4±6}{2} tenglamasini yeching, bunda ± musbat. 4 ni 6 ga qo'shish.

$$d=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$d=5$$

d=\frac{4±6}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 6 ni ayirish.

$$d=-\frac{2}{2}$$

-2 ni 2 ga bo'lish.

$$d=-1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 5 ga va x_{2} uchun -1 ga bo‘ling.

$$d^{2}-4d-5=\left(d-5\right)\left(d-\left(-1\right)\right)$$

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

$$d^{2}-4d-5=\left(d-5\right)\left(d+1\right)$$

Baholash

$$\left(d-5\right)\left(d+1\right)$$