(x-2)(x+1)=4 eching

$$(x-2)(x+1)=4$$

x uchun yechish

$$x=-2$$

$$x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-x-2=4$$

Ikkala tarafdan 4 ni ayirish.

$$x^{2}-x-2-4=0$$

-6 olish uchun -2 dan 4 ni ayirish.

$$x^{2}-x-6=0$$

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 -6 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-6\right)}}{2}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+24}}{2}$$

1 ni 24 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{25}}{2}$$

25 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±5}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±5}{2}$$

x=\frac{1±5}{2} tenglamasini yeching, bunda ± musbat. 1 ni 5 ga qo'shish.

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

6 ni 2 ga bo'lish.

$$x=3$$

x=\frac{1±5}{2} tenglamasini yeching, bunda ± manfiy. 1 dan 5 ni ayirish.

$$x=-\frac{4}{2}$$

-4 ni 2 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

$$x=3 x=-2$$

Kvadratni yakunlash bo'yicha qadamlar

x-2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-x-2=4$$

2 ni ikki tarafga qo’shing.

$$x^{2}-x=4+2$$

6 olish uchun 4 va 2'ni qo'shing.

$$x^{2}-x=6$$

-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.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=6+\left(-\frac{1}{2}\right)^{2}$$

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

$$x^{2}-x+\frac{1}{4}=6+\frac{1}{4}$$

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

$$x^{2}-x+\frac{1}{4}=\frac{25}{4}$$

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.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{5}{2} x-\frac{1}{2}=-\frac{5}{2}$$

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

$$x=3 x=-2$$