x+2x+2/x=14000 eching

$$x + 2 x + \frac { 2 } { x } = 14000$$

x uchun yechish

$$x = \frac{\sqrt{48999994} + 7000}{3} \approx 4666,66652381$$

$$x=\frac{7000-\sqrt{48999994}}{3}\approx 0,000142857$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$xx+2xx+2=14000x$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+2xx+2=14000x$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+2x^{2}+2=14000x$$

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

$$3x^{2}+2=14000x$$

Ikkala tarafdan 14000x ni ayirish.

$$3x^{2}+2-14000x=0$$

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.

$$3x^{2}-14000x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -14000 ni b va 2 ni c bilan almashtiring.

$$x=\frac{-\left(-14000\right)±\sqrt{\left(-14000\right)^{2}-4\times 3\times 2}}{2\times 3}$$

-14000 kvadratini chiqarish.

$$x=\frac{-\left(-14000\right)±\sqrt{196000000-4\times 3\times 2}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-14000\right)±\sqrt{196000000-12\times 2}}{2\times 3}$$

-12 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-14000\right)±\sqrt{196000000-24}}{2\times 3}$$

196000000 ni -24 ga qo'shish.

$$x=\frac{-\left(-14000\right)±\sqrt{195999976}}{2\times 3}$$

195999976 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-14000\right)±2\sqrt{48999994}}{2\times 3}$$

-14000 ning teskarisi 14000 ga teng.

$$x=\frac{14000±2\sqrt{48999994}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{14000±2\sqrt{48999994}}{6}$$

x=\frac{14000±2\sqrt{48999994}}{6} tenglamasini yeching, bunda ± musbat. 14000 ni 2\sqrt{48999994} ga qo'shish.

$$x=\frac{2\sqrt{48999994}+14000}{6}$$

14000+2\sqrt{48999994} ni 6 ga bo'lish.

$$x=\frac{\sqrt{48999994}+7000}{3}$$

x=\frac{14000±2\sqrt{48999994}}{6} tenglamasini yeching, bunda ± manfiy. 14000 dan 2\sqrt{48999994} ni ayirish.

$$x=\frac{14000-2\sqrt{48999994}}{6}$$

14000-2\sqrt{48999994} ni 6 ga bo'lish.

$$x=\frac{7000-\sqrt{48999994}}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{48999994}+7000}{3} x=\frac{7000-\sqrt{48999994}}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$xx+2xx+2=14000x$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+2xx+2=14000x$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+2x^{2}+2=14000x$$

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

$$3x^{2}+2=14000x$$

Ikkala tarafdan 14000x ni ayirish.

$$3x^{2}+2-14000x=0$$

Ikkala tarafdan 2 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$3x^{2}-14000x=-2$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-14000x}{3}=-\frac{2}{3}$$

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

$$x^{2}-\frac{14000}{3}x=-\frac{2}{3}$$

-\frac{14000}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7000}{3} olish uchun. Keyin, -\frac{7000}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{14000}{3}x+\left(-\frac{7000}{3}\right)^{2}=-\frac{2}{3}+\left(-\frac{7000}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7000}{3} kvadratini chiqarish.

$$x^{2}-\frac{14000}{3}x+\frac{49000000}{9}=-\frac{2}{3}+\frac{49000000}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{2}{3} ni \frac{49000000}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{14000}{3}x+\frac{49000000}{9}=\frac{48999994}{9}$$

x^{2}-\frac{14000}{3}x+\frac{49000000}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{7000}{3}\right)^{2}=\frac{48999994}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7000}{3}\right)^{2}}=\sqrt{\frac{48999994}{9}}$$

Qisqartirish.

$$x-\frac{7000}{3}=\frac{\sqrt{48999994}}{3} x-\frac{7000}{3}=-\frac{\sqrt{48999994}}{3}$$

\frac{7000}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{48999994}+7000}{3} x=\frac{7000-\sqrt{48999994}}{3}$$