7x+1=6/x eching

$$7 x + 1 = \frac { 6 } { x }$$

x uchun yechish

$$x=-1$$

$$x=\frac{6}{7}\approx 0,857142857$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$7xx+x=6$$

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

$$7x^{2}+x=6$$

Ikkala tarafdan 6 ni ayirish.

$$7x^{2}+x-6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, 1 ni b va -6 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\times 7\left(-6\right)}}{2\times 7}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\times 7\left(-6\right)}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1-28\left(-6\right)}}{2\times 7}$$

-28 ni -6 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+168}}{2\times 7}$$

1 ni 168 ga qo'shish.

$$x=\frac{-1±\sqrt{169}}{2\times 7}$$

169 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±13}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{-1±13}{14}$$

x=\frac{-1±13}{14} tenglamasini yeching, bunda ± musbat. -1 ni 13 ga qo'shish.

$$x=\frac{12}{14}$$

\frac{12}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{6}{7}$$

x=\frac{-1±13}{14} tenglamasini yeching, bunda ± manfiy. -1 dan 13 ni ayirish.

$$x=-\frac{14}{14}$$

-14 ni 14 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=\frac{6}{7} x=-1$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$7xx+x=6$$

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

$$7x^{2}+x=6$$

Ikki tarafini 7 ga bo‘ling.

$$\frac{7x^{2}+x}{7}=\frac{6}{7}$$

7 ga bo'lish 7 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1}{7}x=\frac{6}{7}$$

\frac{1}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{14} olish uchun. Keyin, \frac{1}{14} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{7}x+\left(\frac{1}{14}\right)^{2}=\frac{6}{7}+\left(\frac{1}{14}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{14} kvadratini chiqarish.

$$x^{2}+\frac{1}{7}x+\frac{1}{196}=\frac{6}{7}+\frac{1}{196}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{6}{7} ni \frac{1}{196} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{1}{7}x+\frac{1}{196}=\frac{169}{196}$$

x^{2}+\frac{1}{7}x+\frac{1}{196} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{14}\right)^{2}=\frac{169}{196}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{14}\right)^{2}}=\sqrt{\frac{169}{196}}$$

Qisqartirish.

$$x+\frac{1}{14}=\frac{13}{14} x+\frac{1}{14}=-\frac{13}{14}$$

Tenglamaning ikkala tarafidan \frac{1}{14} ni ayirish.

$$x=\frac{6}{7} x=-1$$