6z^2-13z+6 eching

$$6 z ^ { 2 } - 13 z + 6$$

Omil

$$\left(2z-3\right)\left(3z-2\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 6z^{2}+az+bz+6 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-13 ab=6\times 6=36$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. 36-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

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

Har bir juftlik yigʻindisini hisoblang.

$$-1-36=-37 -2-18=-20 -3-12=-15 -4-9=-13 -6-6=-12$$

Yechim – -13 yigʻindisini beruvchi juftlik.

$$a=-9 b=-4$$

6z^{2}-13z+6 ni \left(6z^{2}-9z\right)+\left(-4z+6\right) sifatida qaytadan yozish.

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

Birinchi guruhda 3z ni va ikkinchi guruhda -2 ni faktordan chiqaring.

$$3z\left(2z-3\right)-2\left(2z-3\right)$$

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

$$\left(2z-3\right)\left(3z-2\right)$$

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.

$$6z^{2}-13z+6=0$$

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.

$$z=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 6\times 6}}{2\times 6}$$

-13 kvadratini chiqarish.

$$z=\frac{-\left(-13\right)±\sqrt{169-4\times 6\times 6}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$z=\frac{-\left(-13\right)±\sqrt{169-24\times 6}}{2\times 6}$$

-24 ni 6 marotabaga ko'paytirish.

$$z=\frac{-\left(-13\right)±\sqrt{169-144}}{2\times 6}$$

169 ni -144 ga qo'shish.

$$z=\frac{-\left(-13\right)±\sqrt{25}}{2\times 6}$$

25 ning kvadrat ildizini chiqarish.

$$z=\frac{-\left(-13\right)±5}{2\times 6}$$

-13 ning teskarisi 13 ga teng.

$$z=\frac{13±5}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$z=\frac{13±5}{12}$$

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

$$z=\frac{18}{12}$$

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

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

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

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

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

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

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

$$6z^{2}-13z+6=6\left(z-\frac{3}{2}\right)\left(z-\frac{2}{3}\right)$$

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

$$6z^{2}-13z+6=6\times \frac{2z-3}{2}\left(z-\frac{2}{3}\right)$$

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

$$6z^{2}-13z+6=6\times \frac{2z-3}{2}\times \frac{3z-2}{3}$$

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

$$6z^{2}-13z+6=6\times \frac{\left(2z-3\right)\left(3z-2\right)}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$6z^{2}-13z+6=6\times \frac{\left(2z-3\right)\left(3z-2\right)}{6}$$

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

$$6z^{2}-13z+6=\left(2z-3\right)\left(3z-2\right)$$

Baholash

$$\left(2z-3\right)\left(3z-2\right)$$