360/n-1+360/n+2=6 eching

$$\frac { 360 } { n - 1 } + \frac { 360 } { n + 2 } = 6$$

n uchun yechish

$$n = \frac{3 \sqrt{1601} + 119}{2} \approx 119,518747071$$

$$n=\frac{119-3\sqrt{1601}}{2}\approx -0,518747071$$

Kvadrat tenglamalaridan foydalanish qoidalari

n qiymati -2,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(n-1\right)\left(n+2\right) ga, n-1,n+2 ning eng kichik karralisiga ko‘paytiring.

$$\left(n+2\right)\times 360+\left(n-1\right)\times 360=6\left(n-1\right)\left(n+2\right)$$

n+2 ga 360 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$360n+720+\left(n-1\right)\times 360=6\left(n-1\right)\left(n+2\right)$$

n-1 ga 360 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$360n+720+360n-360=6\left(n-1\right)\left(n+2\right)$$

720n ni olish uchun 360n va 360n ni birlashtirish.

$$720n+720-360=6\left(n-1\right)\left(n+2\right)$$

360 olish uchun 720 dan 360 ni ayirish.

$$720n+360=6\left(n-1\right)\left(n+2\right)$$

6 ga n-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$720n+360=\left(6n-6\right)\left(n+2\right)$$

6n-6 ga n+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$720n+360=6n^{2}+6n-12$$

Ikkala tarafdan 6n^{2} ni ayirish.

$$720n+360-6n^{2}=6n-12$$

Ikkala tarafdan 6n ni ayirish.

$$720n+360-6n^{2}-6n=-12$$

714n ni olish uchun 720n va -6n ni birlashtirish.

$$714n+360-6n^{2}=-12$$

12 ni ikki tarafga qo’shing.

$$714n+360-6n^{2}+12=0$$

372 olish uchun 360 va 12'ni qo'shing.

$$714n+372-6n^{2}=0$$

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.

$$-6n^{2}+714n+372=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -6 ni a, 714 ni b va 372 ni c bilan almashtiring.

$$n=\frac{-714±\sqrt{714^{2}-4\left(-6\right)\times 372}}{2\left(-6\right)}$$

714 kvadratini chiqarish.

$$n=\frac{-714±\sqrt{509796-4\left(-6\right)\times 372}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$n=\frac{-714±\sqrt{509796+24\times 372}}{2\left(-6\right)}$$

24 ni 372 marotabaga ko'paytirish.

$$n=\frac{-714±\sqrt{509796+8928}}{2\left(-6\right)}$$

509796 ni 8928 ga qo'shish.

$$n=\frac{-714±\sqrt{518724}}{2\left(-6\right)}$$

518724 ning kvadrat ildizini chiqarish.

$$n=\frac{-714±18\sqrt{1601}}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$n=\frac{-714±18\sqrt{1601}}{-12}$$

n=\frac{-714±18\sqrt{1601}}{-12} tenglamasini yeching, bunda ± musbat. -714 ni 18\sqrt{1601} ga qo'shish.

$$n=\frac{18\sqrt{1601}-714}{-12}$$

-714+18\sqrt{1601} ni -12 ga bo'lish.

$$n=\frac{119-3\sqrt{1601}}{2}$$

n=\frac{-714±18\sqrt{1601}}{-12} tenglamasini yeching, bunda ± manfiy. -714 dan 18\sqrt{1601} ni ayirish.

$$n=\frac{-18\sqrt{1601}-714}{-12}$$

-714-18\sqrt{1601} ni -12 ga bo'lish.

$$n=\frac{3\sqrt{1601}+119}{2}$$

Tenglama yechildi.

$$n=\frac{119-3\sqrt{1601}}{2} n=\frac{3\sqrt{1601}+119}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

n qiymati -2,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(n-1\right)\left(n+2\right) ga, n-1,n+2 ning eng kichik karralisiga ko‘paytiring.

$$\left(n+2\right)\times 360+\left(n-1\right)\times 360=6\left(n-1\right)\left(n+2\right)$$

n+2 ga 360 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$360n+720+\left(n-1\right)\times 360=6\left(n-1\right)\left(n+2\right)$$

n-1 ga 360 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$360n+720+360n-360=6\left(n-1\right)\left(n+2\right)$$

720n ni olish uchun 360n va 360n ni birlashtirish.

$$720n+720-360=6\left(n-1\right)\left(n+2\right)$$

360 olish uchun 720 dan 360 ni ayirish.

$$720n+360=6\left(n-1\right)\left(n+2\right)$$

6 ga n-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$720n+360=\left(6n-6\right)\left(n+2\right)$$

6n-6 ga n+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$720n+360=6n^{2}+6n-12$$

Ikkala tarafdan 6n^{2} ni ayirish.

$$720n+360-6n^{2}=6n-12$$

Ikkala tarafdan 6n ni ayirish.

$$720n+360-6n^{2}-6n=-12$$

714n ni olish uchun 720n va -6n ni birlashtirish.

$$714n+360-6n^{2}=-12$$

Ikkala tarafdan 360 ni ayirish.

$$714n-6n^{2}=-12-360$$

-372 olish uchun -12 dan 360 ni ayirish.

$$714n-6n^{2}=-372$$

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

$$-6n^{2}+714n=-372$$

Ikki tarafini -6 ga bo‘ling.

$$\frac{-6n^{2}+714n}{-6}=-\frac{372}{-6}$$

-6 ga bo'lish -6 ga ko'paytirishni bekor qiladi.

$$n^{2}+\frac{714}{-6}n=-\frac{372}{-6}$$

714 ni -6 ga bo'lish.

$$n^{2}-119n=-\frac{372}{-6}$$

-372 ni -6 ga bo'lish.

$$n^{2}-119n=62$$

-119 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{119}{2} olish uchun. Keyin, -\frac{119}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}-119n+\left(-\frac{119}{2}\right)^{2}=62+\left(-\frac{119}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{119}{2} kvadratini chiqarish.

$$n^{2}-119n+\frac{14161}{4}=62+\frac{14161}{4}$$

62 ni \frac{14161}{4} ga qo'shish.

$$n^{2}-119n+\frac{14161}{4}=\frac{14409}{4}$$

n^{2}-119n+\frac{14161}{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.

$$\left(n-\frac{119}{2}\right)^{2}=\frac{14409}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{119}{2}\right)^{2}}=\sqrt{\frac{14409}{4}}$$

Qisqartirish.

$$n-\frac{119}{2}=\frac{3\sqrt{1601}}{2} n-\frac{119}{2}=-\frac{3\sqrt{1601}}{2}$$

\frac{119}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$n=\frac{3\sqrt{1601}+119}{2} n=\frac{119-3\sqrt{1601}}{2}$$