(x-3)(x-2)=2 eching

$$( x - 3 ) ( x - 2 ) = 2$$

x uchun yechish

$$x=1$$

$$x=4$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-3 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-5x+6=2$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}-5x+6-2=0$$

4 olish uchun 6 dan 2 ni ayirish.

$$x^{2}-5x+4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -5 ni b va 4 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 4}}{2}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 4}}{2}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25-16}}{2}$$

25 ni -16 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{9}}{2}$$

9 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±3}{2}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±3}{2}$$

x=\frac{5±3}{2} tenglamasini yeching, bunda ± musbat. 5 ni 3 ga qo'shish.

$$x=\frac{8}{2}$$

8 ni 2 ga bo'lish.

$$x=4$$

x=\frac{5±3}{2} tenglamasini yeching, bunda ± manfiy. 5 dan 3 ni ayirish.

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

2 ni 2 ga bo'lish.

$$x=1$$

Tenglama yechildi.

$$x=4 x=1$$

Kvadratni yakunlash bo'yicha qadamlar

x-3 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-5x+6=2$$

Ikkala tarafdan 6 ni ayirish.

$$x^{2}-5x=2-6$$

-4 olish uchun 2 dan 6 ni ayirish.

$$x^{2}-5x=-4$$

-5 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{2} olish uchun. Keyin, -\frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=-4+\left(-\frac{5}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{2} kvadratini chiqarish.

$$x^{2}-5x+\frac{25}{4}=-4+\frac{25}{4}$$

-4 ni \frac{25}{4} ga qo'shish.

$$x^{2}-5x+\frac{25}{4}=\frac{9}{4}$$

x^{2}-5x+\frac{25}{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.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

$$x-\frac{5}{2}=\frac{3}{2} x-\frac{5}{2}=-\frac{3}{2}$$

\frac{5}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=4 x=1$$