x^2-17x-60? eching

$$x ^ { 2 } - 17 x - 60 ?$$

Omil

$$\left(x-20\right)\left(x+3\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-60 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-17 ab=1\left(-60\right)=-60$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -60-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-60 2,-30 3,-20 4,-15 5,-12 6,-10$$

Har bir juftlik yigʻindisini hisoblang.

$$1-60=-59 2-30=-28 3-20=-17 4-15=-11 5-12=-7 6-10=-4$$

Yechim – -17 yigʻindisini beruvchi juftlik.

$$a=-20 b=3$$

x^{2}-17x-60 ni \left(x^{2}-20x\right)+\left(3x-60\right) sifatida qaytadan yozish.

$$\left(x^{2}-20x\right)+\left(3x-60\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$x\left(x-20\right)+3\left(x-20\right)$$

Distributiv funktsiyasidan foydalangan holda x-20 umumiy terminini chiqaring.

$$\left(x-20\right)\left(x+3\right)$$

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.

$$x^{2}-17x-60=0$$

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.

$$x=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\left(-60\right)}}{2}$$

-17 kvadratini chiqarish.

$$x=\frac{-\left(-17\right)±\sqrt{289-4\left(-60\right)}}{2}$$

-4 ni -60 marotabaga ko'paytirish.

$$x=\frac{-\left(-17\right)±\sqrt{289+240}}{2}$$

289 ni 240 ga qo'shish.

$$x=\frac{-\left(-17\right)±\sqrt{529}}{2}$$

529 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-17\right)±23}{2}$$

-17 ning teskarisi 17 ga teng.

$$x=\frac{17±23}{2}$$

x=\frac{17±23}{2} tenglamasini yeching, bunda ± musbat. 17 ni 23 ga qo'shish.

$$x=\frac{40}{2}$$

40 ni 2 ga bo'lish.

$$x=20$$

x=\frac{17±23}{2} tenglamasini yeching, bunda ± manfiy. 17 dan 23 ni ayirish.

$$x=-\frac{6}{2}$$

-6 ni 2 ga bo'lish.

$$x=-3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 20 ga va x_{2} uchun -3 ga bo‘ling.

$$x^{2}-17x-60=\left(x-20\right)\left(x-\left(-3\right)\right)$$

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

$$x^{2}-17x-60=\left(x-20\right)\left(x+3\right)$$

Baholash

$$\left(x-20\right)\left(x+3\right)$$