473^-4=x^2/64-x eching

$${ 473 }^{ -4 } = \frac{ { x }^{ 2 } }{ 64-x }$$

x uchun yechish

$$x=\frac{\sqrt{12813994352897}-1}{100109330882}\approx 0,000035758$$

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882}\approx -0,000035758$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 64 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -x+64 ga ko'paytirish.

$$\left(-x+64\right)\times 473^{-4}=x^{2}$$

-4 daraja ko‘rsatkichini 473 ga hisoblang va \frac{1}{50054665441} ni qiymatni oling.

$$\left(-x+64\right)\times \frac{1}{50054665441}=x^{2}$$

-x+64 ga \frac{1}{50054665441} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}-x^{2}=0$$

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.

$$-x^{2}-\frac{1}{50054665441}x+\frac{64}{50054665441}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -\frac{1}{50054665441} ni b va \frac{64}{50054665441} ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\left(-\frac{1}{50054665441}\right)^{2}-4\left(-1\right)\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{50054665441} kvadratini chiqarish.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}-4\left(-1\right)\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}+4\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

4 ni \frac{64}{50054665441} marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}+\frac{256}{50054665441}}}{2\left(-1\right)}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{2505469532410439724481} ni \frac{256}{50054665441} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{12813994352897}{2505469532410439724481}}}{2\left(-1\right)}$$

\frac{12813994352897}{2505469532410439724481} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\frac{\sqrt{12813994352897}}{50054665441}}{2\left(-1\right)}$$

-\frac{1}{50054665441} ning teskarisi \frac{1}{50054665441} ga teng.

$$x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2}$$

x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2} tenglamasini yeching, bunda ± musbat. \frac{1}{50054665441} ni \frac{\sqrt{12813994352897}}{50054665441} ga qo'shish.

$$x=\frac{\sqrt{12813994352897}+1}{-2\times 50054665441}$$

\frac{1+\sqrt{12813994352897}}{50054665441} ni -2 ga bo'lish.

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882}$$

x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2} tenglamasini yeching, bunda ± manfiy. \frac{1}{50054665441} dan \frac{\sqrt{12813994352897}}{50054665441} ni ayirish.

$$x=\frac{1-\sqrt{12813994352897}}{-2\times 50054665441}$$

\frac{1-\sqrt{12813994352897}}{50054665441} ni -2 ga bo'lish.

$$x=\frac{\sqrt{12813994352897}-1}{100109330882}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882} x=\frac{\sqrt{12813994352897}-1}{100109330882}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 64 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -x+64 ga ko'paytirish.

$$\left(-x+64\right)\times 473^{-4}=x^{2}$$

-4 daraja ko‘rsatkichini 473 ga hisoblang va \frac{1}{50054665441} ni qiymatni oling.

$$\left(-x+64\right)\times \frac{1}{50054665441}=x^{2}$$

-x+64 ga \frac{1}{50054665441} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}-x^{2}=0$$

Ikkala tarafdan \frac{64}{50054665441} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-\frac{1}{50054665441}x-x^{2}=-\frac{64}{50054665441}$$

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

$$-x^{2}-\frac{1}{50054665441}x=-\frac{64}{50054665441}$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-\frac{1}{50054665441}x}{-1}=-\frac{\frac{64}{50054665441}}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{\frac{1}{50054665441}}{-1}\right)x=-\frac{\frac{64}{50054665441}}{-1}$$

-\frac{1}{50054665441} ni -1 ga bo'lish.

$$x^{2}+\frac{1}{50054665441}x=-\frac{\frac{64}{50054665441}}{-1}$$

-\frac{64}{50054665441} ni -1 ga bo'lish.

$$x^{2}+\frac{1}{50054665441}x=\frac{64}{50054665441}$$

\frac{1}{50054665441} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{100109330882} olish uchun. Keyin, \frac{1}{100109330882} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{50054665441}x+\left(\frac{1}{100109330882}\right)^{2}=\frac{64}{50054665441}+\left(\frac{1}{100109330882}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{100109330882} kvadratini chiqarish.

$$x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924}=\frac{64}{50054665441}+\frac{1}{10021878129641758897924}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{64}{50054665441} ni \frac{1}{10021878129641758897924} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924}=\frac{12813994352897}{10021878129641758897924}$$

x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{100109330882}\right)^{2}=\frac{12813994352897}{10021878129641758897924}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{100109330882}\right)^{2}}=\sqrt{\frac{12813994352897}{10021878129641758897924}}$$

Qisqartirish.

$$x+\frac{1}{100109330882}=\frac{\sqrt{12813994352897}}{100109330882} x+\frac{1}{100109330882}=-\frac{\sqrt{12813994352897}}{100109330882}$$

Tenglamaning ikkala tarafidan \frac{1}{100109330882} ni ayirish.

$$x=\frac{\sqrt{12813994352897}-1}{100109330882} x=\frac{-\sqrt{12813994352897}-1}{100109330882}$$