18u^2-u-5 eching

$$18 u ^ { 2 } - u - 5$$

Omil

$$\left(9u-5\right)\left(2u+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 18u^{2}+au+bu-5 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-1 ab=18\left(-5\right)=-90$$

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.

$$1,-90 2,-45 3,-30 5,-18 6,-15 9,-10$$

Har bir juftlik yigʻindisini hisoblang.

$$1-90=-89 2-45=-43 3-30=-27 5-18=-13 6-15=-9 9-10=-1$$

Yechim – -1 yigʻindisini beruvchi juftlik.

$$a=-10 b=9$$

18u^{2}-u-5 ni \left(18u^{2}-10u\right)+\left(9u-5\right) sifatida qaytadan yozish.

$$\left(18u^{2}-10u\right)+\left(9u-5\right)$$

18u^{2}-10u ichida 2u ni ajrating.

$$2u\left(9u-5\right)+9u-5$$

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

$$\left(9u-5\right)\left(2u+1\right)$$

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.

$$18u^{2}-u-5=0$$

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.

$$u=\frac{-\left(-1\right)±\sqrt{1-4\times 18\left(-5\right)}}{2\times 18}$$

-4 ni 18 marotabaga ko'paytirish.

$$u=\frac{-\left(-1\right)±\sqrt{1-72\left(-5\right)}}{2\times 18}$$

-72 ni -5 marotabaga ko'paytirish.

$$u=\frac{-\left(-1\right)±\sqrt{1+360}}{2\times 18}$$

1 ni 360 ga qo'shish.

$$u=\frac{-\left(-1\right)±\sqrt{361}}{2\times 18}$$

361 ning kvadrat ildizini chiqarish.

$$u=\frac{-\left(-1\right)±19}{2\times 18}$$

-1 ning teskarisi 1 ga teng.

$$u=\frac{1±19}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$u=\frac{1±19}{36}$$

u=\frac{1±19}{36} tenglamasini yeching, bunda ± musbat. 1 ni 19 ga qo'shish.

$$u=\frac{20}{36}$$

\frac{20}{36} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

u=\frac{1±19}{36} tenglamasini yeching, bunda ± manfiy. 1 dan 19 ni ayirish.

$$u=-\frac{18}{36}$$

\frac{-18}{36} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$u=-\frac{1}{2}$$

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

$$18u^{2}-u-5=18\left(u-\frac{5}{9}\right)\left(u-\left(-\frac{1}{2}\right)\right)$$

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

$$18u^{2}-u-5=18\left(u-\frac{5}{9}\right)\left(u+\frac{1}{2}\right)$$

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

$$18u^{2}-u-5=18\times \frac{9u-5}{9}\left(u+\frac{1}{2}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{2} ni u ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$18u^{2}-u-5=18\times \frac{9u-5}{9}\times \frac{2u+1}{2}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{9u-5}{9} ni \frac{2u+1}{2} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$18u^{2}-u-5=18\times \frac{\left(9u-5\right)\left(2u+1\right)}{9\times 2}$$

9 ni 2 marotabaga ko'paytirish.

$$18u^{2}-u-5=18\times \frac{\left(9u-5\right)\left(2u+1\right)}{18}$$

18 va 18 ichida eng katta umumiy 18 faktorini bekor qiling.

$$18u^{2}-u-5=\left(9u-5\right)\left(2u+1\right)$$

Baholash

$$\left(9u-5\right)\left(2u+1\right)$$