24w^2-23w-630 eching

$$24 w ^ { 2 } - 23 w - 630$$

Omil

$$\left(8w-45\right)\left(3w+14\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 24w^{2}+aw+bw-630 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-23 ab=24\left(-630\right)=-15120$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -15120-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-15120 2,-7560 3,-5040 4,-3780 5,-3024 6,-2520 7,-2160 8,-1890 9,-1680 10,-1512 12,-1260 14,-1080 15,-1008 16,-945 18,-840 20,-756 21,-720 24,-630 27,-560 28,-540 30,-504 35,-432 36,-420 40,-378 42,-360 45,-336 48,-315 54,-280 56,-270 60,-252 63,-240 70,-216 72,-210 80,-189 84,-180 90,-168 105,-144 108,-140 112,-135 120,-126$$

Har bir juftlik yigʻindisini hisoblang.

$$1-15120=-15119 2-7560=-7558 3-5040=-5037 4-3780=-3776 5-3024=-3019 6-2520=-2514 7-2160=-2153 8-1890=-1882 9-1680=-1671 10-1512=-1502 12-1260=-1248 14-1080=-1066 15-1008=-993 16-945=-929 18-840=-822 20-756=-736 21-720=-699 24-630=-606 27-560=-533 28-540=-512 30-504=-474 35-432=-397 36-420=-384 40-378=-338 42-360=-318 45-336=-291 48-315=-267 54-280=-226 56-270=-214 60-252=-192 63-240=-177 70-216=-146 72-210=-138 80-189=-109 84-180=-96 90-168=-78 105-144=-39 108-140=-32 112-135=-23 120-126=-6$$

Yechim – -23 yigʻindisini beruvchi juftlik.

$$a=-135 b=112$$

24w^{2}-23w-630 ni \left(24w^{2}-135w\right)+\left(112w-630\right) sifatida qaytadan yozish.

$$\left(24w^{2}-135w\right)+\left(112w-630\right)$$

Birinchi guruhda 3w ni va ikkinchi guruhda 14 ni faktordan chiqaring.

$$3w\left(8w-45\right)+14\left(8w-45\right)$$

Distributiv funktsiyasidan foydalangan holda 8w-45 umumiy terminini chiqaring.

$$\left(8w-45\right)\left(3w+14\right)$$

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.

$$24w^{2}-23w-630=0$$

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.

$$w=\frac{-\left(-23\right)±\sqrt{\left(-23\right)^{2}-4\times 24\left(-630\right)}}{2\times 24}$$

-23 kvadratini chiqarish.

$$w=\frac{-\left(-23\right)±\sqrt{529-4\times 24\left(-630\right)}}{2\times 24}$$

-4 ni 24 marotabaga ko'paytirish.

$$w=\frac{-\left(-23\right)±\sqrt{529-96\left(-630\right)}}{2\times 24}$$

-96 ni -630 marotabaga ko'paytirish.

$$w=\frac{-\left(-23\right)±\sqrt{529+60480}}{2\times 24}$$

529 ni 60480 ga qo'shish.

$$w=\frac{-\left(-23\right)±\sqrt{61009}}{2\times 24}$$

61009 ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-23\right)±247}{2\times 24}$$

-23 ning teskarisi 23 ga teng.

$$w=\frac{23±247}{2\times 24}$$

2 ni 24 marotabaga ko'paytirish.

$$w=\frac{23±247}{48}$$

w=\frac{23±247}{48} tenglamasini yeching, bunda ± musbat. 23 ni 247 ga qo'shish.

$$w=\frac{270}{48}$$

\frac{270}{48} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w=\frac{45}{8}$$

w=\frac{23±247}{48} tenglamasini yeching, bunda ± manfiy. 23 dan 247 ni ayirish.

$$w=-\frac{224}{48}$$

\frac{-224}{48} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w=-\frac{14}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{45}{8} ga va x_{2} uchun -\frac{14}{3} ga bo‘ling.

$$24w^{2}-23w-630=24\left(w-\frac{45}{8}\right)\left(w-\left(-\frac{14}{3}\right)\right)$$

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

$$24w^{2}-23w-630=24\left(w-\frac{45}{8}\right)\left(w+\frac{14}{3}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{45}{8} ni w dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$24w^{2}-23w-630=24\times \frac{8w-45}{8}\left(w+\frac{14}{3}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{14}{3} ni w ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$24w^{2}-23w-630=24\times \frac{8w-45}{8}\times \frac{3w+14}{3}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{8w-45}{8} ni \frac{3w+14}{3} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$24w^{2}-23w-630=24\times \frac{\left(8w-45\right)\left(3w+14\right)}{8\times 3}$$

8 ni 3 marotabaga ko'paytirish.

$$24w^{2}-23w-630=24\times \frac{\left(8w-45\right)\left(3w+14\right)}{24}$$

24 va 24 ichida eng katta umumiy 24 faktorini bekor qiling.

$$24w^{2}-23w-630=\left(8w-45\right)\left(3w+14\right)$$

Baholash

$$\left(8w-45\right)\left(3w+14\right)$$