Omil
\left(6t-5\right)\left(3t+1\right)
Baholash
\left(6t-5\right)\left(3t+1\right)
Baham ko'rish
Klipbordga nusxa olish
a+b=-9 ab=18\left(-5\right)=-90
Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 18t^{2}+at+bt-5 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.
1,-90 2,-45 3,-30 5,-18 6,-15 9,-10
ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -90-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.
1-90=-89 2-45=-43 3-30=-27 5-18=-13 6-15=-9 9-10=-1
Har bir juftlik yigʻindisini hisoblang.
a=-15 b=6
Yechim – -9 yigʻindisini beruvchi juftlik.
\left(18t^{2}-15t\right)+\left(6t-5\right)
18t^{2}-9t-5 ni \left(18t^{2}-15t\right)+\left(6t-5\right) sifatida qaytadan yozish.
3t\left(6t-5\right)+6t-5
18t^{2}-15t ichida 3t ni ajrating.
\left(6t-5\right)\left(3t+1\right)
Distributiv funktsiyasidan foydalangan holda 6t-5 umumiy terminini chiqaring.
18t^{2}-9t-5=0
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.
t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 18\left(-5\right)}}{2\times 18}
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(-9\right)±\sqrt{81-4\times 18\left(-5\right)}}{2\times 18}
-9 kvadratini chiqarish.
t=\frac{-\left(-9\right)±\sqrt{81-72\left(-5\right)}}{2\times 18}
-4 ni 18 marotabaga ko'paytirish.
t=\frac{-\left(-9\right)±\sqrt{81+360}}{2\times 18}
-72 ni -5 marotabaga ko'paytirish.
t=\frac{-\left(-9\right)±\sqrt{441}}{2\times 18}
81 ni 360 ga qo'shish.
t=\frac{-\left(-9\right)±21}{2\times 18}
441 ning kvadrat ildizini chiqarish.
t=\frac{9±21}{2\times 18}
-9 ning teskarisi 9 ga teng.
t=\frac{9±21}{36}
2 ni 18 marotabaga ko'paytirish.
t=\frac{30}{36}
t=\frac{9±21}{36} tenglamasini yeching, bunda ± musbat. 9 ni 21 ga qo'shish.
t=\frac{5}{6}
\frac{30}{36} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
t=-\frac{12}{36}
t=\frac{9±21}{36} tenglamasini yeching, bunda ± manfiy. 9 dan 21 ni ayirish.
t=-\frac{1}{3}
\frac{-12}{36} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
18t^{2}-9t-5=18\left(t-\frac{5}{6}\right)\left(t-\left(-\frac{1}{3}\right)\right)
ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5}{6} ga va x_{2} uchun -\frac{1}{3} ga bo‘ling.
18t^{2}-9t-5=18\left(t-\frac{5}{6}\right)\left(t+\frac{1}{3}\right)
p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.
18t^{2}-9t-5=18\times \frac{6t-5}{6}\left(t+\frac{1}{3}\right)
Umumiy maxrajni topib va suratlarni ayirib \frac{5}{6} ni t dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.
18t^{2}-9t-5=18\times \frac{6t-5}{6}\times \frac{3t+1}{3}
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.
18t^{2}-9t-5=18\times \frac{\left(6t-5\right)\left(3t+1\right)}{6\times 3}
Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{6t-5}{6} ni \frac{3t+1}{3} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.
18t^{2}-9t-5=18\times \frac{\left(6t-5\right)\left(3t+1\right)}{18}
6 ni 3 marotabaga ko'paytirish.
18t^{2}-9t-5=\left(6t-5\right)\left(3t+1\right)
18 va 18 ichida eng katta umumiy 18 faktorini bekor qiling.
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