-72x^2+17x-1 eching

$$-72 { x }^{ 2 } +17x-1$$

Omil

$$\left(1-9x\right)\left(8x-1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -72x^{2}+ax+bx-1 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=17 ab=-72\left(-1\right)=72$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 72-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,72 2,36 3,24 4,18 6,12 8,9$$

Har bir juftlik yigʻindisini hisoblang.

$$1+72=73 2+36=38 3+24=27 4+18=22 6+12=18 8+9=17$$

Yechim – 17 yigʻindisini beruvchi juftlik.

$$a=9 b=8$$

-72x^{2}+17x-1 ni \left(-72x^{2}+9x\right)+\left(8x-1\right) sifatida qaytadan yozish.

$$\left(-72x^{2}+9x\right)+\left(8x-1\right)$$

-72x^{2}+9x ichida -9x ni ajrating.

$$-9x\left(8x-1\right)+8x-1$$

Distributiv funktsiyasidan foydalangan holda 8x-1 umumiy terminini chiqaring.

$$\left(8x-1\right)\left(-9x+1\right)$$

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.

$$-72x^{2}+17x-1=0$$

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.

$$x=\frac{-17±\sqrt{17^{2}-4\left(-72\right)\left(-1\right)}}{2\left(-72\right)}$$

17 kvadratini chiqarish.

$$x=\frac{-17±\sqrt{289-4\left(-72\right)\left(-1\right)}}{2\left(-72\right)}$$

-4 ni -72 marotabaga ko'paytirish.

$$x=\frac{-17±\sqrt{289+288\left(-1\right)}}{2\left(-72\right)}$$

288 ni -1 marotabaga ko'paytirish.

$$x=\frac{-17±\sqrt{289-288}}{2\left(-72\right)}$$

289 ni -288 ga qo'shish.

$$x=\frac{-17±\sqrt{1}}{2\left(-72\right)}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-17±1}{2\left(-72\right)}$$

2 ni -72 marotabaga ko'paytirish.

$$x=\frac{-17±1}{-144}$$

x=\frac{-17±1}{-144} tenglamasini yeching, bunda ± musbat. -17 ni 1 ga qo'shish.

$$x=-\frac{16}{-144}$$

\frac{-16}{-144} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{9}$$

x=\frac{-17±1}{-144} tenglamasini yeching, bunda ± manfiy. -17 dan 1 ni ayirish.

$$x=-\frac{18}{-144}$$

\frac{-18}{-144} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1}{9} ga va x_{2} uchun \frac{1}{8} ga bo‘ling.

$$-72x^{2}+17x-1=-72\left(x-\frac{1}{9}\right)\left(x-\frac{1}{8}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{9} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$-72x^{2}+17x-1=-72\times \frac{-9x+1}{-9}\left(x-\frac{1}{8}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{8} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$-72x^{2}+17x-1=-72\times \frac{-9x+1}{-9}\times \frac{-8x+1}{-8}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{-9x+1}{-9} ni \frac{-8x+1}{-8} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$-72x^{2}+17x-1=-72\times \frac{\left(-9x+1\right)\left(-8x+1\right)}{-9\left(-8\right)}$$

-9 ni -8 marotabaga ko'paytirish.

$$-72x^{2}+17x-1=-72\times \frac{\left(-9x+1\right)\left(-8x+1\right)}{72}$$

-72 va 72 ichida eng katta umumiy 72 faktorini bekor qiling.

$$-72x^{2}+17x-1=-\left(-9x+1\right)\left(-8x+1\right)$$

Baholash

$$\left(1-9x\right)\left(8x-1\right)$$