x-56+64/x=0 eching

$$x-56+ \frac{ 64 }{ x } =0$$

x uchun yechish

$$x=12\sqrt{5}+28\approx 54,83281573$$

$$x=28-12\sqrt{5}\approx 1,16718427$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$xx+x\left(-56\right)+64=0$$

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

$$x^{2}+x\left(-56\right)+64=0$$

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.

$$x^{2}-56x+64=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -56 ni b va 64 ni c bilan almashtiring.

$$x=\frac{-\left(-56\right)±\sqrt{\left(-56\right)^{2}-4\times 64}}{2}$$

-56 kvadratini chiqarish.

$$x=\frac{-\left(-56\right)±\sqrt{3136-4\times 64}}{2}$$

-4 ni 64 marotabaga ko'paytirish.

$$x=\frac{-\left(-56\right)±\sqrt{3136-256}}{2}$$

3136 ni -256 ga qo'shish.

$$x=\frac{-\left(-56\right)±\sqrt{2880}}{2}$$

2880 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-56\right)±24\sqrt{5}}{2}$$

-56 ning teskarisi 56 ga teng.

$$x=\frac{56±24\sqrt{5}}{2}$$

x=\frac{56±24\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat. 56 ni 24\sqrt{5} ga qo'shish.

$$x=\frac{24\sqrt{5}+56}{2}$$

56+24\sqrt{5} ni 2 ga bo'lish.

$$x=12\sqrt{5}+28$$

x=\frac{56±24\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy. 56 dan 24\sqrt{5} ni ayirish.

$$x=\frac{56-24\sqrt{5}}{2}$$

56-24\sqrt{5} ni 2 ga bo'lish.

$$x=28-12\sqrt{5}$$

Tenglama yechildi.

$$x=12\sqrt{5}+28 x=28-12\sqrt{5}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$xx+x\left(-56\right)+64=0$$

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

$$x^{2}+x\left(-56\right)+64=0$$

Ikkala tarafdan 64 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}+x\left(-56\right)=-64$$

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

$$x^{2}-56x=-64$$

-56 ni bo‘lish, x shartining koeffitsienti, 2 ga -28 olish uchun. Keyin, -28 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-56x+\left(-28\right)^{2}=-64+\left(-28\right)^{2}$$

-28 kvadratini chiqarish.

$$x^{2}-56x+784=-64+784$$

-64 ni 784 ga qo'shish.

$$x^{2}-56x+784=720$$

x^{2}-56x+784 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-28\right)^{2}=720$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-28\right)^{2}}=\sqrt{720}$$

Qisqartirish.

$$x-28=12\sqrt{5} x-28=-12\sqrt{5}$$

28 ni tenglamaning ikkala tarafiga qo'shish.

$$x=12\sqrt{5}+28 x=28-12\sqrt{5}$$