-1+2d^2-d eching

$$- 1 + 2 d ^ { 2 } - d$$

Omil

$$\left(d-1\right)\left(2d+1\right)$$

Yechim qadamlari

Polinomni standart shaklga keltirish uchun uni qayta tartiblang. Shartlarni eng yuqoridan eng pastki qiymat ko'rsatgichiga joylashtirish.

$$2d^{2}-d-1$$

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 2d^{2}+ad+bd-1 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

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

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.

$$a=-2 b=1$$

2d^{2}-d-1 ni \left(2d^{2}-2d\right)+\left(d-1\right) sifatida qaytadan yozish.

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

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

$$2d\left(d-1\right)+d-1$$

Distributiv funktsiyasidan foydalangan holda d-1 umumiy terminini chiqaring.

$$\left(d-1\right)\left(2d+1\right)$$

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.

$$2d^{2}-d-1=0$$

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.

$$d=\frac{-\left(-1\right)±\sqrt{1-4\times 2\left(-1\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$d=\frac{-\left(-1\right)±\sqrt{1-8\left(-1\right)}}{2\times 2}$$

-8 ni -1 marotabaga ko'paytirish.

$$d=\frac{-\left(-1\right)±\sqrt{1+8}}{2\times 2}$$

1 ni 8 ga qo'shish.

$$d=\frac{-\left(-1\right)±\sqrt{9}}{2\times 2}$$

9 ning kvadrat ildizini chiqarish.

$$d=\frac{-\left(-1\right)±3}{2\times 2}$$

-1 ning teskarisi 1 ga teng.

$$d=\frac{1±3}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$d=\frac{1±3}{4}$$

d=\frac{1±3}{4} tenglamasini yeching, bunda ± musbat. 1 ni 3 ga qo'shish.

$$d=\frac{4}{4}$$

4 ni 4 ga bo'lish.

$$d=1$$

d=\frac{1±3}{4} tenglamasini yeching, bunda ± manfiy. 1 dan 3 ni ayirish.

$$d=-\frac{2}{4}$$

\frac{-2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$d=-\frac{1}{2}$$

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

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

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

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

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{2} ni d ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$2d^{2}-d-1=2\left(d-1\right)\times \frac{2d+1}{2}$$

2 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

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

Baholash

$$\left(d-1\right)\left(2d+1\right)$$