v^2+16v-17 eching

$$v ^ { 2 } + 16 v - 17$$

Omil

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

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda v^{2}+av+bv-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 musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

$$a=-1 b=17$$

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

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

Birinchi guruhda v ni va ikkinchi guruhda 17 ni faktordan chiqaring.

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

Distributiv funktsiyasidan foydalangan holda v-1 umumiy terminini chiqaring.

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

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.

$$v^{2}+16v-17=0$$

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.

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

16 kvadratini chiqarish.

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

-4 ni -17 marotabaga ko'paytirish.

$$v=\frac{-16±\sqrt{256+68}}{2}$$

256 ni 68 ga qo'shish.

$$v=\frac{-16±\sqrt{324}}{2}$$

324 ning kvadrat ildizini chiqarish.

$$v=\frac{-16±18}{2}$$

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

$$v=\frac{2}{2}$$

2 ni 2 ga bo'lish.

$$v=1$$

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

$$v=-\frac{34}{2}$$

-34 ni 2 ga bo'lish.

$$v=-17$$

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

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

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

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

Baholash

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