56s^2+17s-3 eching

$$56 s ^ { 2 } + 17 s - 3$$

Omil

$$\left(8s-1\right)\left(7s+3\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 56s^{2}+as+bs-3 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=17 ab=56\left(-3\right)=-168$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. -168-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,168 -2,84 -3,56 -4,42 -6,28 -7,24 -8,21 -12,14$$

Har bir juftlik yigʻindisini hisoblang.

$$-1+168=167 -2+84=82 -3+56=53 -4+42=38 -6+28=22 -7+24=17 -8+21=13 -12+14=2$$

Yechim – 17 yigʻindisini beruvchi juftlik.

$$a=-7 b=24$$

56s^{2}+17s-3 ni \left(56s^{2}-7s\right)+\left(24s-3\right) sifatida qaytadan yozish.

$$\left(56s^{2}-7s\right)+\left(24s-3\right)$$

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

$$7s\left(8s-1\right)+3\left(8s-1\right)$$

Distributiv funktsiyasidan foydalangan holda 8s-1 umumiy terminini chiqaring.

$$\left(8s-1\right)\left(7s+3\right)$$

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.

$$56s^{2}+17s-3=0$$

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.

$$s=\frac{-17±\sqrt{17^{2}-4\times 56\left(-3\right)}}{2\times 56}$$

17 kvadratini chiqarish.

$$s=\frac{-17±\sqrt{289-4\times 56\left(-3\right)}}{2\times 56}$$

-4 ni 56 marotabaga ko'paytirish.

$$s=\frac{-17±\sqrt{289-224\left(-3\right)}}{2\times 56}$$

-224 ni -3 marotabaga ko'paytirish.

$$s=\frac{-17±\sqrt{289+672}}{2\times 56}$$

289 ni 672 ga qo'shish.

$$s=\frac{-17±\sqrt{961}}{2\times 56}$$

961 ning kvadrat ildizini chiqarish.

$$s=\frac{-17±31}{2\times 56}$$

2 ni 56 marotabaga ko'paytirish.

$$s=\frac{-17±31}{112}$$

s=\frac{-17±31}{112} tenglamasini yeching, bunda ± musbat. -17 ni 31 ga qo'shish.

$$s=\frac{14}{112}$$

\frac{14}{112} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s=\frac{1}{8}$$

s=\frac{-17±31}{112} tenglamasini yeching, bunda ± manfiy. -17 dan 31 ni ayirish.

$$s=-\frac{48}{112}$$

\frac{-48}{112} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1}{8} ga va x_{2} uchun -\frac{3}{7} ga bo‘ling.

$$56s^{2}+17s-3=56\left(s-\frac{1}{8}\right)\left(s-\left(-\frac{3}{7}\right)\right)$$

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

$$56s^{2}+17s-3=56\left(s-\frac{1}{8}\right)\left(s+\frac{3}{7}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{8} ni s dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$56s^{2}+17s-3=56\times \frac{8s-1}{8}\left(s+\frac{3}{7}\right)$$

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

$$56s^{2}+17s-3=56\times \frac{8s-1}{8}\times \frac{7s+3}{7}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{8s-1}{8} ni \frac{7s+3}{7} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$56s^{2}+17s-3=56\times \frac{\left(8s-1\right)\left(7s+3\right)}{8\times 7}$$

8 ni 7 marotabaga ko'paytirish.

$$56s^{2}+17s-3=56\times \frac{\left(8s-1\right)\left(7s+3\right)}{56}$$

56 va 56 ichida eng katta umumiy 56 faktorini bekor qiling.

$$56s^{2}+17s-3=\left(8s-1\right)\left(7s+3\right)$$

Baholash

$$\left(8s-1\right)\left(7s+3\right)$$