3t^2-2t-1 eching

$$3 t ^ { 2 } - 2 t - 1$$

Omil

$$\left(t-1\right)\left(3t+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 3t^{2}+at+bt-1 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=3\left(-1\right)=-3$$

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.

$$a=-3 b=1$$

3t^{2}-2t-1 ni \left(3t^{2}-3t\right)+\left(t-1\right) sifatida qaytadan yozish.

$$\left(3t^{2}-3t\right)+\left(t-1\right)$$

3t^{2}-3t ichida 3t ni ajrating.

$$3t\left(t-1\right)+t-1$$

Distributiv funktsiyasidan foydalangan holda t-1 umumiy terminini chiqaring.

$$\left(t-1\right)\left(3t+1\right)$$

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.

$$3t^{2}-2t-1=0$$

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.

$$t=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

-2 kvadratini chiqarish.

$$t=\frac{-\left(-2\right)±\sqrt{4-4\times 3\left(-1\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$t=\frac{-\left(-2\right)±\sqrt{4-12\left(-1\right)}}{2\times 3}$$

-12 ni -1 marotabaga ko'paytirish.

$$t=\frac{-\left(-2\right)±\sqrt{4+12}}{2\times 3}$$

4 ni 12 ga qo'shish.

$$t=\frac{-\left(-2\right)±\sqrt{16}}{2\times 3}$$

16 ning kvadrat ildizini chiqarish.

$$t=\frac{-\left(-2\right)±4}{2\times 3}$$

-2 ning teskarisi 2 ga teng.

$$t=\frac{2±4}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$t=\frac{2±4}{6}$$

t=\frac{2±4}{6} tenglamasini yeching, bunda ± musbat. 2 ni 4 ga qo'shish.

$$t=\frac{6}{6}$$

6 ni 6 ga bo'lish.

$$t=1$$

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

$$t=-\frac{2}{6}$$

\frac{-2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$t=-\frac{1}{3}$$

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}{3} ga bo‘ling.

$$3t^{2}-2t-1=3\left(t-1\right)\left(t-\left(-\frac{1}{3}\right)\right)$$

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

$$3t^{2}-2t-1=3\left(t-1\right)\left(t+\frac{1}{3}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{3} ni t ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$3t^{2}-2t-1=3\left(t-1\right)\times \frac{3t+1}{3}$$

3 va 3 ichida eng katta umumiy 3 faktorini bekor qiling.

$$3t^{2}-2t-1=\left(t-1\right)\left(3t+1\right)$$

Baholash

$$\left(t-1\right)\left(3t+1\right)$$