x+1/x=100 eching

$$x + \frac { 1 } { x } = 100$$

x uchun yechish

$$x=7\sqrt{51}+50\approx 99,989999$$

$$x=50-7\sqrt{51}\approx 0,010001$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$xx+1=100x$$

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

$$x^{2}+1=100x$$

Ikkala tarafdan 100x ni ayirish.

$$x^{2}+1-100x=0$$

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.

$$x^{2}-100x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -100 ni b va 1 ni c bilan almashtiring.

$$x=\frac{-\left(-100\right)±\sqrt{\left(-100\right)^{2}-4}}{2}$$

-100 kvadratini chiqarish.

$$x=\frac{-\left(-100\right)±\sqrt{10000-4}}{2}$$

10000 ni -4 ga qo'shish.

$$x=\frac{-\left(-100\right)±\sqrt{9996}}{2}$$

9996 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-100\right)±14\sqrt{51}}{2}$$

-100 ning teskarisi 100 ga teng.

$$x=\frac{100±14\sqrt{51}}{2}$$

x=\frac{100±14\sqrt{51}}{2} tenglamasini yeching, bunda ± musbat. 100 ni 14\sqrt{51} ga qo'shish.

$$x=\frac{14\sqrt{51}+100}{2}$$

100+14\sqrt{51} ni 2 ga bo'lish.

$$x=7\sqrt{51}+50$$

x=\frac{100±14\sqrt{51}}{2} tenglamasini yeching, bunda ± manfiy. 100 dan 14\sqrt{51} ni ayirish.

$$x=\frac{100-14\sqrt{51}}{2}$$

100-14\sqrt{51} ni 2 ga bo'lish.

$$x=50-7\sqrt{51}$$

Tenglama yechildi.

$$x=7\sqrt{51}+50 x=50-7\sqrt{51}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$xx+1=100x$$

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

$$x^{2}+1=100x$$

Ikkala tarafdan 100x ni ayirish.

$$x^{2}+1-100x=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-100x=-1$$

-100 ni bo‘lish, x shartining koeffitsienti, 2 ga -50 olish uchun. Keyin, -50 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-100x+\left(-50\right)^{2}=-1+\left(-50\right)^{2}$$

-50 kvadratini chiqarish.

$$x^{2}-100x+2500=-1+2500$$

-1 ni 2500 ga qo'shish.

$$x^{2}-100x+2500=2499$$

x^{2}-100x+2500 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-50\right)^{2}=2499$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-50\right)^{2}}=\sqrt{2499}$$

Qisqartirish.

$$x-50=7\sqrt{51} x-50=-7\sqrt{51}$$

50 ni tenglamaning ikkala tarafiga qo'shish.

$$x=7\sqrt{51}+50 x=50-7\sqrt{51}$$