(x+2)/frac{6{x}}=8 eching

$$\frac { ( x + 2 ) } { \frac { 6 } { x } } = 8$$

x uchun yechish

$$x=-8$$

$$x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. x+2 ni \frac{6}{x} ga bo'lish x+2 ga k'paytirish \frac{6}{x} ga qaytarish.

$$\frac{\left(x+2\right)x}{6}=8$$

x+2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x^{2}+2x}{6}=8$$

\frac{1}{6}x^{2}+\frac{1}{3}x natijani olish uchun x^{2}+2x ning har bir ifodasini 6 ga bo‘ling.

$$\frac{1}{6}x^{2}+\frac{1}{3}x=8$$

Ikkala tarafdan 8 ni ayirish.

$$\frac{1}{6}x^{2}+\frac{1}{3}x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{6} ni a, \frac{1}{3} ni b va -8 ni c bilan almashtiring.

$$x=\frac{-\frac{1}{3}±\sqrt{\left(\frac{1}{3}\right)^{2}-4\times \frac{1}{6}\left(-8\right)}}{2\times \frac{1}{6}}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{3} kvadratini chiqarish.

$$x=\frac{-\frac{1}{3}±\sqrt{\frac{1}{9}-4\times \frac{1}{6}\left(-8\right)}}{2\times \frac{1}{6}}$$

-4 ni \frac{1}{6} marotabaga ko'paytirish.

$$x=\frac{-\frac{1}{3}±\sqrt{\frac{1}{9}-\frac{2}{3}\left(-8\right)}}{2\times \frac{1}{6}}$$

-\frac{2}{3} ni -8 marotabaga ko'paytirish.

$$x=\frac{-\frac{1}{3}±\sqrt{\frac{1}{9}+\frac{16}{3}}}{2\times \frac{1}{6}}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{9} ni \frac{16}{3} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{-\frac{1}{3}±\sqrt{\frac{49}{9}}}{2\times \frac{1}{6}}$$

\frac{49}{9} ning kvadrat ildizini chiqarish.

$$x=\frac{-\frac{1}{3}±\frac{7}{3}}{2\times \frac{1}{6}}$$

2 ni \frac{1}{6} marotabaga ko'paytirish.

$$x=\frac{-\frac{1}{3}±\frac{7}{3}}{\frac{1}{3}}$$

x=\frac{-\frac{1}{3}±\frac{7}{3}}{\frac{1}{3}} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{3} ni \frac{7}{3} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{2}{\frac{1}{3}}$$

2 ni \frac{1}{3} ga bo'lish 2 ga k'paytirish \frac{1}{3} ga qaytarish.

$$x=6$$

x=\frac{-\frac{1}{3}±\frac{7}{3}}{\frac{1}{3}} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{7}{3} ni -\frac{1}{3} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=-\frac{\frac{8}{3}}{\frac{1}{3}}$$

-\frac{8}{3} ni \frac{1}{3} ga bo'lish -\frac{8}{3} ga k'paytirish \frac{1}{3} ga qaytarish.

$$x=-8$$

Tenglama yechildi.

$$x=6 x=-8$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. x+2 ni \frac{6}{x} ga bo'lish x+2 ga k'paytirish \frac{6}{x} ga qaytarish.

$$\frac{\left(x+2\right)x}{6}=8$$

x+2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x^{2}+2x}{6}=8$$

\frac{1}{6}x^{2}+\frac{1}{3}x natijani olish uchun x^{2}+2x ning har bir ifodasini 6 ga bo‘ling.

$$\frac{1}{6}x^{2}+\frac{1}{3}x=8$$

Ikkala tarafini 6 ga ko‘paytiring.

$$\frac{\frac{1}{6}x^{2}+\frac{1}{3}x}{\frac{1}{6}}=\frac{8}{\frac{1}{6}}$$

\frac{1}{6} ga bo'lish \frac{1}{6} ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{\frac{1}{3}}{\frac{1}{6}}x=\frac{8}{\frac{1}{6}}$$

\frac{1}{3} ni \frac{1}{6} ga bo'lish \frac{1}{3} ga k'paytirish \frac{1}{6} ga qaytarish.

$$x^{2}+2x=\frac{8}{\frac{1}{6}}$$

8 ni \frac{1}{6} ga bo'lish 8 ga k'paytirish \frac{1}{6} ga qaytarish.

$$x^{2}+2x=48$$

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

$$x^{2}+2x+1^{2}=48+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=48+1$$

48 ni 1 ga qo'shish.

$$x^{2}+2x+1=49$$

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

$$\left(x+1\right)^{2}=49$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{49}$$

Qisqartirish.

$$x+1=7 x+1=-7$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=6 x=-8$$