3v^2-8v-35 eching

$$3 v ^ { 2 } - 8 v - 35$$

Omil

$$\left(v-5\right)\left(3v+7\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 3v^{2}+av+bv-35 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-8 ab=3\left(-35\right)=-105$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -105-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-105 3,-35 5,-21 7,-15$$

Har bir juftlik yigʻindisini hisoblang.

$$1-105=-104 3-35=-32 5-21=-16 7-15=-8$$

Yechim – -8 yigʻindisini beruvchi juftlik.

$$a=-15 b=7$$

3v^{2}-8v-35 ni \left(3v^{2}-15v\right)+\left(7v-35\right) sifatida qaytadan yozish.

$$\left(3v^{2}-15v\right)+\left(7v-35\right)$$

Birinchi guruhda 3v ni va ikkinchi guruhda 7 ni faktordan chiqaring.

$$3v\left(v-5\right)+7\left(v-5\right)$$

Distributiv funktsiyasidan foydalangan holda v-5 umumiy terminini chiqaring.

$$\left(v-5\right)\left(3v+7\right)$$

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.

$$3v^{2}-8v-35=0$$

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.

$$v=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 3\left(-35\right)}}{2\times 3}$$

-8 kvadratini chiqarish.

$$v=\frac{-\left(-8\right)±\sqrt{64-4\times 3\left(-35\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$v=\frac{-\left(-8\right)±\sqrt{64-12\left(-35\right)}}{2\times 3}$$

-12 ni -35 marotabaga ko'paytirish.

$$v=\frac{-\left(-8\right)±\sqrt{64+420}}{2\times 3}$$

64 ni 420 ga qo'shish.

$$v=\frac{-\left(-8\right)±\sqrt{484}}{2\times 3}$$

484 ning kvadrat ildizini chiqarish.

$$v=\frac{-\left(-8\right)±22}{2\times 3}$$

-8 ning teskarisi 8 ga teng.

$$v=\frac{8±22}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$v=\frac{8±22}{6}$$

v=\frac{8±22}{6} tenglamasini yeching, bunda ± musbat. 8 ni 22 ga qo'shish.

$$v=\frac{30}{6}$$

30 ni 6 ga bo'lish.

$$v=5$$

v=\frac{8±22}{6} tenglamasini yeching, bunda ± manfiy. 8 dan 22 ni ayirish.

$$v=-\frac{14}{6}$$

\frac{-14}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$v=-\frac{7}{3}$$

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 -\frac{7}{3} ga bo‘ling.

$$3v^{2}-8v-35=3\left(v-5\right)\left(v-\left(-\frac{7}{3}\right)\right)$$

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

$$3v^{2}-8v-35=3\left(v-5\right)\left(v+\frac{7}{3}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{7}{3} ni v ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$3v^{2}-8v-35=3\left(v-5\right)\times \frac{3v+7}{3}$$

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

$$3v^{2}-8v-35=\left(v-5\right)\left(3v+7\right)$$

Baholash

$$\left(v-5\right)\left(3v+7\right)$$