3n^2-363n+10620=0 eching

$$3 n ^ { 2 } - 363 n + 10620 = 0$$

n uchun yechish

$$n = \frac{\sqrt{481} + 121}{2} \approx 71,4658561$$

$$n = \frac{121 - \sqrt{481}}{2} \approx 49,5341439$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$3n^{2}-363n+10620=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -363 ni b va 10620 ni c bilan almashtiring.

$$n=\frac{-\left(-363\right)±\sqrt{\left(-363\right)^{2}-4\times 3\times 10620}}{2\times 3}$$

-363 kvadratini chiqarish.

$$n=\frac{-\left(-363\right)±\sqrt{131769-4\times 3\times 10620}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$n=\frac{-\left(-363\right)±\sqrt{131769-12\times 10620}}{2\times 3}$$

-12 ni 10620 marotabaga ko'paytirish.

$$n=\frac{-\left(-363\right)±\sqrt{131769-127440}}{2\times 3}$$

131769 ni -127440 ga qo'shish.

$$n=\frac{-\left(-363\right)±\sqrt{4329}}{2\times 3}$$

4329 ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-363\right)±3\sqrt{481}}{2\times 3}$$

-363 ning teskarisi 363 ga teng.

$$n=\frac{363±3\sqrt{481}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$n=\frac{363±3\sqrt{481}}{6}$$

n=\frac{363±3\sqrt{481}}{6} tenglamasini yeching, bunda ± musbat. 363 ni 3\sqrt{481} ga qo'shish.

$$n=\frac{3\sqrt{481}+363}{6}$$

363+3\sqrt{481} ni 6 ga bo'lish.

$$n=\frac{\sqrt{481}+121}{2}$$

n=\frac{363±3\sqrt{481}}{6} tenglamasini yeching, bunda ± manfiy. 363 dan 3\sqrt{481} ni ayirish.

$$n=\frac{363-3\sqrt{481}}{6}$$

363-3\sqrt{481} ni 6 ga bo'lish.

$$n=\frac{121-\sqrt{481}}{2}$$

Tenglama yechildi.

$$n=\frac{\sqrt{481}+121}{2} n=\frac{121-\sqrt{481}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$3n^{2}-363n+10620=0$$

Tenglamaning ikkala tarafidan 10620 ni ayirish.

$$3n^{2}-363n+10620-10620=-10620$$

O‘zidan 10620 ayirilsa 0 qoladi.

$$3n^{2}-363n=-10620$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3n^{2}-363n}{3}=-\frac{10620}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$n^{2}+\left(-\frac{363}{3}\right)n=-\frac{10620}{3}$$

-363 ni 3 ga bo'lish.

$$n^{2}-121n=-\frac{10620}{3}$$

-10620 ni 3 ga bo'lish.

$$n^{2}-121n=-3540$$

-121 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{121}{2} olish uchun. Keyin, -\frac{121}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}-121n+\left(-\frac{121}{2}\right)^{2}=-3540+\left(-\frac{121}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{121}{2} kvadratini chiqarish.

$$n^{2}-121n+\frac{14641}{4}=-3540+\frac{14641}{4}$$

-3540 ni \frac{14641}{4} ga qo'shish.

$$n^{2}-121n+\frac{14641}{4}=\frac{481}{4}$$

n^{2}-121n+\frac{14641}{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.

$$\left(n-\frac{121}{2}\right)^{2}=\frac{481}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{121}{2}\right)^{2}}=\sqrt{\frac{481}{4}}$$

Qisqartirish.

$$n-\frac{121}{2}=\frac{\sqrt{481}}{2} n-\frac{121}{2}=-\frac{\sqrt{481}}{2}$$

\frac{121}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$n=\frac{\sqrt{481}+121}{2} n=\frac{121-\sqrt{481}}{2}$$