4=x^2-3x-4 eching

$$4 = x ^ { 2 } - 3 x - 4$$

x uchun yechish

$$x = \frac{\sqrt{41} + 3}{2} \approx 4,701562119$$

$$x=\frac{3-\sqrt{41}}{2}\approx -1,701562119$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-3x-4=4$$

Ikkala tarafdan 4 ni ayirish.

$$x^{2}-3x-4-4=0$$

-8 olish uchun -4 dan 4 ni ayirish.

$$x^{2}-3x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va -8 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-8\right)}}{2}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-8\right)}}{2}$$

-4 ni -8 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+32}}{2}$$

9 ni 32 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{41}}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±\sqrt{41}}{2}$$

x=\frac{3±\sqrt{41}}{2} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{41} ga qo'shish.

$$x=\frac{\sqrt{41}+3}{2}$$

x=\frac{3±\sqrt{41}}{2} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{41} ni ayirish.

$$x=\frac{3-\sqrt{41}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{41}+3}{2} x=\frac{3-\sqrt{41}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-3x-4=4$$

4 ni ikki tarafga qo’shing.

$$x^{2}-3x=4+4$$

8 olish uchun 4 va 4'ni qo'shing.

$$x^{2}-3x=8$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=8+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=8+\frac{9}{4}$$

8 ni \frac{9}{4} ga qo'shish.

$$x^{2}-3x+\frac{9}{4}=\frac{41}{4}$$

x^{2}-3x+\frac{9}{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.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{41}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{41}{4}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{\sqrt{41}}{2} x-\frac{3}{2}=-\frac{\sqrt{41}}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{41}+3}{2} x=\frac{3-\sqrt{41}}{2}$$