4x+7/x=3 eching

$$4x+ \frac{ 7 }{ x } =3$$

x uchun yechish (complex solution)

$$x=\frac{3+\sqrt{103}i}{8}\approx 0,375+1,268611446i$$

$$x=\frac{-\sqrt{103}i+3}{8}\approx 0,375-1,268611446i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$4xx+7=3x$$

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

$$4x^{2}+7=3x$$

Ikkala tarafdan 3x ni ayirish.

$$4x^{2}+7-3x=0$$

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.

$$4x^{2}-3x+7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -3 ni b va 7 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 4\times 7}}{2\times 4}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\times 4\times 7}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9-16\times 7}}{2\times 4}$$

-16 ni 7 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9-112}}{2\times 4}$$

9 ni -112 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{-103}}{2\times 4}$$

-103 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{103}i}{2\times 4}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±\sqrt{103}i}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{3±\sqrt{103}i}{8}$$

x=\frac{3±\sqrt{103}i}{8} tenglamasini yeching, bunda ± musbat. 3 ni i\sqrt{103} ga qo'shish.

$$x=\frac{3+\sqrt{103}i}{8}$$

x=\frac{3±\sqrt{103}i}{8} tenglamasini yeching, bunda ± manfiy. 3 dan i\sqrt{103} ni ayirish.

$$x=\frac{-\sqrt{103}i+3}{8}$$

Tenglama yechildi.

$$x=\frac{3+\sqrt{103}i}{8} x=\frac{-\sqrt{103}i+3}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$4xx+7=3x$$

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

$$4x^{2}+7=3x$$

Ikkala tarafdan 3x ni ayirish.

$$4x^{2}+7-3x=0$$

Ikkala tarafdan 7 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$4x^{2}-3x=-7$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-3x}{4}=-\frac{7}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{3}{4}x=-\frac{7}{4}$$

-\frac{3}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{8} olish uchun. Keyin, -\frac{3}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{3}{4}x+\left(-\frac{3}{8}\right)^{2}=-\frac{7}{4}+\left(-\frac{3}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{8} kvadratini chiqarish.

$$x^{2}-\frac{3}{4}x+\frac{9}{64}=-\frac{7}{4}+\frac{9}{64}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{7}{4} ni \frac{9}{64} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{3}{4}x+\frac{9}{64}=-\frac{103}{64}$$

x^{2}-\frac{3}{4}x+\frac{9}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{8}\right)^{2}=-\frac{103}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{8}\right)^{2}}=\sqrt{-\frac{103}{64}}$$

Qisqartirish.

$$x-\frac{3}{8}=\frac{\sqrt{103}i}{8} x-\frac{3}{8}=-\frac{\sqrt{103}i}{8}$$

\frac{3}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3+\sqrt{103}i}{8} x=\frac{-\sqrt{103}i+3}{8}$$