-2800+160x-x^2 eching

$$-2800+160x- { x }^{ 2 }$$

Omil

$$\left(20-x\right)\left(x-140\right)$$

Yechim qadamlari

Polinomni standart shaklga keltirish uchun uni qayta tartiblang. Shartlarni eng yuqoridan eng pastki qiymat ko'rsatgichiga joylashtirish.

$$-x^{2}+160x-2800$$

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx-2800 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=160 ab=-\left(-2800\right)=2800$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 2800-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,2800 2,1400 4,700 5,560 7,400 8,350 10,280 14,200 16,175 20,140 25,112 28,100 35,80 40,70 50,56$$

Har bir juftlik yigʻindisini hisoblang.

$$1+2800=2801 2+1400=1402 4+700=704 5+560=565 7+400=407 8+350=358 10+280=290 14+200=214 16+175=191 20+140=160 25+112=137 28+100=128 35+80=115 40+70=110 50+56=106$$

Yechim – 160 yigʻindisini beruvchi juftlik.

$$a=140 b=20$$

-x^{2}+160x-2800 ni \left(-x^{2}+140x\right)+\left(20x-2800\right) sifatida qaytadan yozish.

$$\left(-x^{2}+140x\right)+\left(20x-2800\right)$$

Birinchi guruhda -x ni va ikkinchi guruhda 20 ni faktordan chiqaring.

$$-x\left(x-140\right)+20\left(x-140\right)$$

Distributiv funktsiyasidan foydalangan holda x-140 umumiy terminini chiqaring.

$$\left(x-140\right)\left(-x+20\right)$$

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.

$$-x^{2}+160x-2800=0$$

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.

$$x=\frac{-160±\sqrt{160^{2}-4\left(-1\right)\left(-2800\right)}}{2\left(-1\right)}$$

160 kvadratini chiqarish.

$$x=\frac{-160±\sqrt{25600-4\left(-1\right)\left(-2800\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-160±\sqrt{25600+4\left(-2800\right)}}{2\left(-1\right)}$$

4 ni -2800 marotabaga ko'paytirish.

$$x=\frac{-160±\sqrt{25600-11200}}{2\left(-1\right)}$$

25600 ni -11200 ga qo'shish.

$$x=\frac{-160±\sqrt{14400}}{2\left(-1\right)}$$

14400 ning kvadrat ildizini chiqarish.

$$x=\frac{-160±120}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-160±120}{-2}$$

x=\frac{-160±120}{-2} tenglamasini yeching, bunda ± musbat. -160 ni 120 ga qo'shish.

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

-40 ni -2 ga bo'lish.

$$x=20$$

x=\frac{-160±120}{-2} tenglamasini yeching, bunda ± manfiy. -160 dan 120 ni ayirish.

$$x=-\frac{280}{-2}$$

-280 ni -2 ga bo'lish.

$$x=140$$

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 140 ga bo‘ling.

$$-x^{2}+160x-2800=-\left(x-20\right)\left(x-140\right)$$

Baholash

$$\left(20-x\right)\left(x-140\right)$$