j^2-16j-17 eching

$$j ^ { 2 } - 16 j - 17$$

Omil

$$\left(j-17\right)\left(j+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda j^{2}+aj+bj-17 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-16 ab=1\left(-17\right)=-17$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

$$a=-17 b=1$$

j^{2}-16j-17 ni \left(j^{2}-17j\right)+\left(j-17\right) sifatida qaytadan yozish.

$$\left(j^{2}-17j\right)+\left(j-17\right)$$

j^{2}-17j ichida j ni ajrating.

$$j\left(j-17\right)+j-17$$

Distributiv funktsiyasidan foydalangan holda j-17 umumiy terminini chiqaring.

$$\left(j-17\right)\left(j+1\right)$$

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.

$$j^{2}-16j-17=0$$

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.

$$j=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-17\right)}}{2}$$

-16 kvadratini chiqarish.

$$j=\frac{-\left(-16\right)±\sqrt{256-4\left(-17\right)}}{2}$$

-4 ni -17 marotabaga ko'paytirish.

$$j=\frac{-\left(-16\right)±\sqrt{256+68}}{2}$$

256 ni 68 ga qo'shish.

$$j=\frac{-\left(-16\right)±\sqrt{324}}{2}$$

324 ning kvadrat ildizini chiqarish.

$$j=\frac{-\left(-16\right)±18}{2}$$

-16 ning teskarisi 16 ga teng.

$$j=\frac{16±18}{2}$$

j=\frac{16±18}{2} tenglamasini yeching, bunda ± musbat. 16 ni 18 ga qo'shish.

$$j=\frac{34}{2}$$

34 ni 2 ga bo'lish.

$$j=17$$

j=\frac{16±18}{2} tenglamasini yeching, bunda ± manfiy. 16 dan 18 ni ayirish.

$$j=-\frac{2}{2}$$

-2 ni 2 ga bo'lish.

$$j=-1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 17 ga va x_{2} uchun -1 ga bo‘ling.

$$j^{2}-16j-17=\left(j-17\right)\left(j-\left(-1\right)\right)$$

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

$$j^{2}-16j-17=\left(j-17\right)\left(j+1\right)$$

Baholash

$$\left(j-17\right)\left(j+1\right)$$