6u^2+5u-6 eching

$$6 u ^ { 2 } + 5 u - 6$$

Omil

$$\left(3u-2\right)\left(2u+3\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 6u^{2}+au+bu-6 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=5 ab=6\left(-6\right)=-36$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. -36-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,36 -2,18 -3,12 -4,9 -6,6$$

Har bir juftlik yigʻindisini hisoblang.

$$-1+36=35 -2+18=16 -3+12=9 -4+9=5 -6+6=0$$

Yechim – 5 yigʻindisini beruvchi juftlik.

$$a=-4 b=9$$

6u^{2}+5u-6 ni \left(6u^{2}-4u\right)+\left(9u-6\right) sifatida qaytadan yozish.

$$\left(6u^{2}-4u\right)+\left(9u-6\right)$$

Birinchi guruhda 2u ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$2u\left(3u-2\right)+3\left(3u-2\right)$$

Distributiv funktsiyasidan foydalangan holda 3u-2 umumiy terminini chiqaring.

$$\left(3u-2\right)\left(2u+3\right)$$

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.

$$6u^{2}+5u-6=0$$

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.

$$u=\frac{-5±\sqrt{5^{2}-4\times 6\left(-6\right)}}{2\times 6}$$

5 kvadratini chiqarish.

$$u=\frac{-5±\sqrt{25-4\times 6\left(-6\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$u=\frac{-5±\sqrt{25-24\left(-6\right)}}{2\times 6}$$

-24 ni -6 marotabaga ko'paytirish.

$$u=\frac{-5±\sqrt{25+144}}{2\times 6}$$

25 ni 144 ga qo'shish.

$$u=\frac{-5±\sqrt{169}}{2\times 6}$$

169 ning kvadrat ildizini chiqarish.

$$u=\frac{-5±13}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$u=\frac{-5±13}{12}$$

u=\frac{-5±13}{12} tenglamasini yeching, bunda ± musbat. -5 ni 13 ga qo'shish.

$$u=\frac{8}{12}$$

\frac{8}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$u=\frac{2}{3}$$

u=\frac{-5±13}{12} tenglamasini yeching, bunda ± manfiy. -5 dan 13 ni ayirish.

$$u=-\frac{18}{12}$$

\frac{-18}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$u=-\frac{3}{2}$$

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

$$6u^{2}+5u-6=6\left(u-\frac{2}{3}\right)\left(u-\left(-\frac{3}{2}\right)\right)$$

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

$$6u^{2}+5u-6=6\left(u-\frac{2}{3}\right)\left(u+\frac{3}{2}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{2}{3} ni u dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$6u^{2}+5u-6=6\times \frac{3u-2}{3}\left(u+\frac{3}{2}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni u ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$6u^{2}+5u-6=6\times \frac{3u-2}{3}\times \frac{2u+3}{2}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{3u-2}{3} ni \frac{2u+3}{2} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$6u^{2}+5u-6=6\times \frac{\left(3u-2\right)\left(2u+3\right)}{3\times 2}$$

3 ni 2 marotabaga ko'paytirish.

$$6u^{2}+5u-6=6\times \frac{\left(3u-2\right)\left(2u+3\right)}{6}$$

6 va 6 ichida eng katta umumiy 6 faktorini bekor qiling.

$$6u^{2}+5u-6=\left(3u-2\right)\left(2u+3\right)$$

Baholash

$$\left(3u-2\right)\left(2u+3\right)$$