30s^2-19s-63 eching

$$30 s ^ { 2 } - 19 s - 63$$

Omil

$$\left(5s-9\right)\left(6s+7\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 30s^{2}+as+bs-63 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-19 ab=30\left(-63\right)=-1890$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -1890-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-1890 2,-945 3,-630 5,-378 6,-315 7,-270 9,-210 10,-189 14,-135 15,-126 18,-105 21,-90 27,-70 30,-63 35,-54 42,-45$$

Har bir juftlik yigʻindisini hisoblang.

$$1-1890=-1889 2-945=-943 3-630=-627 5-378=-373 6-315=-309 7-270=-263 9-210=-201 10-189=-179 14-135=-121 15-126=-111 18-105=-87 21-90=-69 27-70=-43 30-63=-33 35-54=-19 42-45=-3$$

Yechim – -19 yigʻindisini beruvchi juftlik.

$$a=-54 b=35$$

30s^{2}-19s-63 ni \left(30s^{2}-54s\right)+\left(35s-63\right) sifatida qaytadan yozish.

$$\left(30s^{2}-54s\right)+\left(35s-63\right)$$

Birinchi guruhda 6s ni va ikkinchi guruhda 7 ni faktordan chiqaring.

$$6s\left(5s-9\right)+7\left(5s-9\right)$$

Distributiv funktsiyasidan foydalangan holda 5s-9 umumiy terminini chiqaring.

$$\left(5s-9\right)\left(6s+7\right)$$

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.

$$30s^{2}-19s-63=0$$

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.

$$s=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}-4\times 30\left(-63\right)}}{2\times 30}$$

-19 kvadratini chiqarish.

$$s=\frac{-\left(-19\right)±\sqrt{361-4\times 30\left(-63\right)}}{2\times 30}$$

-4 ni 30 marotabaga ko'paytirish.

$$s=\frac{-\left(-19\right)±\sqrt{361-120\left(-63\right)}}{2\times 30}$$

-120 ni -63 marotabaga ko'paytirish.

$$s=\frac{-\left(-19\right)±\sqrt{361+7560}}{2\times 30}$$

361 ni 7560 ga qo'shish.

$$s=\frac{-\left(-19\right)±\sqrt{7921}}{2\times 30}$$

7921 ning kvadrat ildizini chiqarish.

$$s=\frac{-\left(-19\right)±89}{2\times 30}$$

-19 ning teskarisi 19 ga teng.

$$s=\frac{19±89}{2\times 30}$$

2 ni 30 marotabaga ko'paytirish.

$$s=\frac{19±89}{60}$$

s=\frac{19±89}{60} tenglamasini yeching, bunda ± musbat. 19 ni 89 ga qo'shish.

$$s=\frac{108}{60}$$

\frac{108}{60} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s=\frac{9}{5}$$

s=\frac{19±89}{60} tenglamasini yeching, bunda ± manfiy. 19 dan 89 ni ayirish.

$$s=-\frac{70}{60}$$

\frac{-70}{60} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s=-\frac{7}{6}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{9}{5} ga va x_{2} uchun -\frac{7}{6} ga bo‘ling.

$$30s^{2}-19s-63=30\left(s-\frac{9}{5}\right)\left(s-\left(-\frac{7}{6}\right)\right)$$

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

$$30s^{2}-19s-63=30\left(s-\frac{9}{5}\right)\left(s+\frac{7}{6}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{9}{5} ni s dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$30s^{2}-19s-63=30\times \frac{5s-9}{5}\left(s+\frac{7}{6}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{7}{6} ni s ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$30s^{2}-19s-63=30\times \frac{5s-9}{5}\times \frac{6s+7}{6}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{5s-9}{5} ni \frac{6s+7}{6} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$30s^{2}-19s-63=30\times \frac{\left(5s-9\right)\left(6s+7\right)}{5\times 6}$$

5 ni 6 marotabaga ko'paytirish.

$$30s^{2}-19s-63=30\times \frac{\left(5s-9\right)\left(6s+7\right)}{30}$$

30 va 30 ichida eng katta umumiy 30 faktorini bekor qiling.

$$30s^{2}-19s-63=\left(5s-9\right)\left(6s+7\right)$$

Baholash

$$\left(5s-9\right)\left(6s+7\right)$$