x^2+121x+120= eching

$$x ^ { 2 } + 121 x + 120 =$$

Omil

$$\left(x+1\right)\left(x+120\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx+120 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=121 ab=1\times 120=120$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 120-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,120 2,60 3,40 4,30 5,24 6,20 8,15 10,12$$

Har bir juftlik yigʻindisini hisoblang.

$$1+120=121 2+60=62 3+40=43 4+30=34 5+24=29 6+20=26 8+15=23 10+12=22$$

Yechim – 121 yigʻindisini beruvchi juftlik.

$$a=1 b=120$$

x^{2}+121x+120 ni \left(x^{2}+x\right)+\left(120x+120\right) sifatida qaytadan yozish.

$$\left(x^{2}+x\right)+\left(120x+120\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 120 ni faktordan chiqaring.

$$x\left(x+1\right)+120\left(x+1\right)$$

Distributiv funktsiyasidan foydalangan holda x+1 umumiy terminini chiqaring.

$$\left(x+1\right)\left(x+120\right)$$

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.

$$x^{2}+121x+120=0$$

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.

$$x=\frac{-121±\sqrt{121^{2}-4\times 120}}{2}$$

121 kvadratini chiqarish.

$$x=\frac{-121±\sqrt{14641-4\times 120}}{2}$$

-4 ni 120 marotabaga ko'paytirish.

$$x=\frac{-121±\sqrt{14641-480}}{2}$$

14641 ni -480 ga qo'shish.

$$x=\frac{-121±\sqrt{14161}}{2}$$

14161 ning kvadrat ildizini chiqarish.

$$x=\frac{-121±119}{2}$$

x=\frac{-121±119}{2} tenglamasini yeching, bunda ± musbat. -121 ni 119 ga qo'shish.

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

-2 ni 2 ga bo'lish.

$$x=-1$$

x=\frac{-121±119}{2} tenglamasini yeching, bunda ± manfiy. -121 dan 119 ni ayirish.

$$x=-\frac{240}{2}$$

-240 ni 2 ga bo'lish.

$$x=-120$$

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 -120 ga bo‘ling.

$$x^{2}+121x+120=\left(x-\left(-1\right)\right)\left(x-\left(-120\right)\right)$$

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

$$x^{2}+121x+120=\left(x+1\right)\left(x+120\right)$$

Baholash

$$\left(x+1\right)\left(x+120\right)$$