n^2-4019n+2009^2=0 eching

$$n ^ { 2 } - 4019 n + 2009 ^ { 2 } = 0$$

n uchun yechish

$$n = \frac{3 \sqrt{893} + 4019}{2} \approx 2054,324658392$$

$$n = \frac{4019 - 3 \sqrt{893}}{2} \approx 1964,675341608$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 2009 ga hisoblang va 4036081 ni qiymatni oling.

$$n^{2}-4019n+4036081=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -4019 ni b va 4036081 ni c bilan almashtiring.

$$n=\frac{-\left(-4019\right)±\sqrt{\left(-4019\right)^{2}-4\times 4036081}}{2}$$

-4019 kvadratini chiqarish.

$$n=\frac{-\left(-4019\right)±\sqrt{16152361-4\times 4036081}}{2}$$

-4 ni 4036081 marotabaga ko'paytirish.

$$n=\frac{-\left(-4019\right)±\sqrt{16152361-16144324}}{2}$$

16152361 ni -16144324 ga qo'shish.

$$n=\frac{-\left(-4019\right)±\sqrt{8037}}{2}$$

8037 ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-4019\right)±3\sqrt{893}}{2}$$

-4019 ning teskarisi 4019 ga teng.

$$n=\frac{4019±3\sqrt{893}}{2}$$

n=\frac{4019±3\sqrt{893}}{2} tenglamasini yeching, bunda ± musbat. 4019 ni 3\sqrt{893} ga qo'shish.

$$n=\frac{3\sqrt{893}+4019}{2}$$

n=\frac{4019±3\sqrt{893}}{2} tenglamasini yeching, bunda ± manfiy. 4019 dan 3\sqrt{893} ni ayirish.

$$n=\frac{4019-3\sqrt{893}}{2}$$

Tenglama yechildi.

$$n=\frac{3\sqrt{893}+4019}{2} n=\frac{4019-3\sqrt{893}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2 daraja ko‘rsatkichini 2009 ga hisoblang va 4036081 ni qiymatni oling.

$$n^{2}-4019n+4036081=0$$

Ikkala tarafdan 4036081 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$n^{2}-4019n=-4036081$$

-4019 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{4019}{2} olish uchun. Keyin, -\frac{4019}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}-4019n+\left(-\frac{4019}{2}\right)^{2}=-4036081+\left(-\frac{4019}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{4019}{2} kvadratini chiqarish.

$$n^{2}-4019n+\frac{16152361}{4}=-4036081+\frac{16152361}{4}$$

-4036081 ni \frac{16152361}{4} ga qo'shish.

$$n^{2}-4019n+\frac{16152361}{4}=\frac{8037}{4}$$

n^{2}-4019n+\frac{16152361}{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.

$$\left(n-\frac{4019}{2}\right)^{2}=\frac{8037}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{4019}{2}\right)^{2}}=\sqrt{\frac{8037}{4}}$$

Qisqartirish.

$$n-\frac{4019}{2}=\frac{3\sqrt{893}}{2} n-\frac{4019}{2}=-\frac{3\sqrt{893}}{2}$$

\frac{4019}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$n=\frac{3\sqrt{893}+4019}{2} n=\frac{4019-3\sqrt{893}}{2}$$