x^2=1x+132 eching

$$x ^ { 2 } = 1 x + 132$$

x uchun yechish

$$x=-11$$

$$x=12$$

Faktorlash qadamlari

Ikkala tarafdan 1x ni ayirish.

$$x^{2}-x=132$$

Ikkala tarafdan 132 ni ayirish.

$$x^{2}-x-132=0$$

Bu tenglamani yechish uchun x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right) formulasi yordamida x^{2}-x-132 ni faktorlang. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-1 ab=-132$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -132-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-132 2,-66 3,-44 4,-33 6,-22 11,-12$$

Har bir juftlik yigʻindisini hisoblang.

$$1-132=-131 2-66=-64 3-44=-41 4-33=-29 6-22=-16 11-12=-1$$

Yechim – -1 yigʻindisini beruvchi juftlik.

$$a=-12 b=11$$

Faktorlangan \left(x+a\right)\left(x+b\right) ifodani olingan qiymatlar bilan qaytadan yozing.

$$\left(x-12\right)\left(x+11\right)$$

Tenglamani yechish uchun x-12=0 va x+11=0 ni yeching.

$$x=12 x=-11$$

Guruhlash orqali faktorlash qadamlari

Ikkala tarafdan 1x ni ayirish.

$$x^{2}-x=132$$

Ikkala tarafdan 132 ni ayirish.

$$x^{2}-x-132=0$$

Tenglamani yechish uchun guruhlash orqali chap qoʻl tomonni faktorlang. Avvalo, chap qoʻl tomon x^{2}+ax+bx-132 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-1 ab=1\left(-132\right)=-132$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -132-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-132 2,-66 3,-44 4,-33 6,-22 11,-12$$

Har bir juftlik yigʻindisini hisoblang.

$$1-132=-131 2-66=-64 3-44=-41 4-33=-29 6-22=-16 11-12=-1$$

Yechim – -1 yigʻindisini beruvchi juftlik.

$$a=-12 b=11$$

x^{2}-x-132 ni \left(x^{2}-12x\right)+\left(11x-132\right) sifatida qaytadan yozish.

$$\left(x^{2}-12x\right)+\left(11x-132\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 11 ni faktordan chiqaring.

$$x\left(x-12\right)+11\left(x-12\right)$$

Distributiv funktsiyasidan foydalangan holda x-12 umumiy terminini chiqaring.

$$\left(x-12\right)\left(x+11\right)$$

Tenglamani yechish uchun x-12=0 va x+11=0 ni yeching.

$$x=12 x=-11$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1x ni ayirish.

$$x^{2}-x=132$$

Ikkala tarafdan 132 ni ayirish.

$$x^{2}-x-132=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1 ni b va -132 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-132\right)}}{2}$$

-4 ni -132 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+528}}{2}$$

1 ni 528 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{529}}{2}$$

529 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±23}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±23}{2}$$

x=\frac{1±23}{2} tenglamasini yeching, bunda ± musbat. 1 ni 23 ga qo'shish.

$$x=\frac{24}{2}$$

24 ni 2 ga bo'lish.

$$x=12$$

x=\frac{1±23}{2} tenglamasini yeching, bunda ± manfiy. 1 dan 23 ni ayirish.

$$x=-\frac{22}{2}$$

-22 ni 2 ga bo'lish.

$$x=-11$$

Tenglama yechildi.

$$x=12 x=-11$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 1x ni ayirish.

$$x^{2}-x=132$$

-1 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{2} olish uchun. Keyin, -\frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=132+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=132+\frac{1}{4}$$

132 ni \frac{1}{4} ga qo'shish.

$$x^{2}-x+\frac{1}{4}=\frac{529}{4}$$

x^{2}-x+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{529}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{529}{4}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{23}{2} x-\frac{1}{2}=-\frac{23}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=12 x=-11$$