9z^2-17z-2 eching

$$9 z ^ { 2 } - 17 z - 2$$

Omil

$$\left(z-2\right)\left(9z+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 9z^{2}+az+bz-2 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-17 ab=9\left(-2\right)=-18$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -18-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-18 2,-9 3,-6$$

Har bir juftlik yigʻindisini hisoblang.

$$1-18=-17 2-9=-7 3-6=-3$$

Yechim – -17 yigʻindisini beruvchi juftlik.

$$a=-18 b=1$$

9z^{2}-17z-2 ni \left(9z^{2}-18z\right)+\left(z-2\right) sifatida qaytadan yozish.

$$\left(9z^{2}-18z\right)+\left(z-2\right)$$

9z^{2}-18z ichida 9z ni ajrating.

$$9z\left(z-2\right)+z-2$$

Distributiv funktsiyasidan foydalangan holda z-2 umumiy terminini chiqaring.

$$\left(z-2\right)\left(9z+1\right)$$

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.

$$9z^{2}-17z-2=0$$

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.

$$z=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 9\left(-2\right)}}{2\times 9}$$

-17 kvadratini chiqarish.

$$z=\frac{-\left(-17\right)±\sqrt{289-4\times 9\left(-2\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$z=\frac{-\left(-17\right)±\sqrt{289-36\left(-2\right)}}{2\times 9}$$

-36 ni -2 marotabaga ko'paytirish.

$$z=\frac{-\left(-17\right)±\sqrt{289+72}}{2\times 9}$$

289 ni 72 ga qo'shish.

$$z=\frac{-\left(-17\right)±\sqrt{361}}{2\times 9}$$

361 ning kvadrat ildizini chiqarish.

$$z=\frac{-\left(-17\right)±19}{2\times 9}$$

-17 ning teskarisi 17 ga teng.

$$z=\frac{17±19}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$z=\frac{17±19}{18}$$

z=\frac{17±19}{18} tenglamasini yeching, bunda ± musbat. 17 ni 19 ga qo'shish.

$$z=\frac{36}{18}$$

36 ni 18 ga bo'lish.

$$z=2$$

z=\frac{17±19}{18} tenglamasini yeching, bunda ± manfiy. 17 dan 19 ni ayirish.

$$z=-\frac{2}{18}$$

\frac{-2}{18} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$z=-\frac{1}{9}$$

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

$$9z^{2}-17z-2=9\left(z-2\right)\left(z-\left(-\frac{1}{9}\right)\right)$$

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

$$9z^{2}-17z-2=9\left(z-2\right)\left(z+\frac{1}{9}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{9} ni z ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$9z^{2}-17z-2=9\left(z-2\right)\times \frac{9z+1}{9}$$

9 va 9 ichida eng katta umumiy 9 faktorini bekor qiling.

$$9z^{2}-17z-2=\left(z-2\right)\left(9z+1\right)$$

Baholash

$$\left(z-2\right)\left(9z+1\right)$$