11/8left(3/11+1/6+frac{3/2right)}{x}=frac{x}{frac{frac{5}{3}-frac{1}{4}+frac{3}{2}}{frac{7}{6}}frac{20}{3}} eching

$$\frac{ \frac{ 11 }{ 8 } \left( \frac{ 3 }{ 11 } + \frac{ 1 }{ 6 } + \frac{ 3 }{ 2 } \right) }{ x } = \frac{ x }{ \frac{ \frac{ 5 }{ 3 } - \frac{ 1 }{ 4 } + \frac{ 3 }{ 2 } }{ \frac{ 7 }{ 6 } } \frac{ 20 }{ 3 } }$$

x uchun yechish

$$x = \frac{20}{3} = 6\frac{2}{3} \approx 6,666666667$$

$$x = -\frac{20}{3} = -6\frac{2}{3} \approx -6,666666667$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$\frac{11}{8}\left(\frac{3}{11}+\frac{1}{6}+\frac{3}{2}\right)=\frac{3}{50}xx$$

11 va 6 ning eng kichik umumiy karralisi 66 ga teng. \frac{3}{11} va \frac{1}{6} ni 66 maxraj bilan kasrlarga aylantirib oling.

$$\frac{11}{8}\left(\frac{18}{66}+\frac{11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

\frac{18}{66} va \frac{11}{66} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{11}{8}\left(\frac{18+11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

29 olish uchun 18 va 11'ni qo'shing.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

66 va 2 ning eng kichik umumiy karralisi 66 ga teng. \frac{29}{66} va \frac{3}{2} ni 66 maxraj bilan kasrlarga aylantirib oling.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{99}{66}\right)=\frac{3}{50}xx$$

\frac{29}{66} va \frac{99}{66} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{11}{8}\times \frac{29+99}{66}=\frac{3}{50}xx$$

128 olish uchun 29 va 99'ni qo'shing.

$$\frac{11}{8}\times \frac{128}{66}=\frac{3}{50}xx$$

\frac{128}{66} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{11}{8}\times \frac{64}{33}=\frac{3}{50}xx$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{11}{8} ni \frac{64}{33} ga ko‘paytiring.

$$\frac{11\times 64}{8\times 33}=\frac{3}{50}xx$$

\frac{11\times 64}{8\times 33} kasridagi ko‘paytirishlarni bajaring.

$$\frac{704}{264}=\frac{3}{50}xx$$

\frac{704}{264} ulushini 88 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{8}{3}=\frac{3}{50}xx$$

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

$$\frac{8}{3}=\frac{3}{50}x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{3}{50}x^{2}=\frac{8}{3}$$

Ikki tarafini \frac{50}{3} va teskari kasri \frac{3}{50} ga ko‘paytiring.

$$x^{2}=\frac{8}{3}\times \frac{50}{3}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{8}{3} ni \frac{50}{3} ga ko‘paytiring.

$$x^{2}=\frac{8\times 50}{3\times 3}$$

\frac{8\times 50}{3\times 3} kasridagi ko‘paytirishlarni bajaring.

$$x^{2}=\frac{400}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{20}{3} x=-\frac{20}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$\frac{11}{8}\left(\frac{3}{11}+\frac{1}{6}+\frac{3}{2}\right)=\frac{3}{50}xx$$

11 va 6 ning eng kichik umumiy karralisi 66 ga teng. \frac{3}{11} va \frac{1}{6} ni 66 maxraj bilan kasrlarga aylantirib oling.

$$\frac{11}{8}\left(\frac{18}{66}+\frac{11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

\frac{18}{66} va \frac{11}{66} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{11}{8}\left(\frac{18+11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

29 olish uchun 18 va 11'ni qo'shing.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

66 va 2 ning eng kichik umumiy karralisi 66 ga teng. \frac{29}{66} va \frac{3}{2} ni 66 maxraj bilan kasrlarga aylantirib oling.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{99}{66}\right)=\frac{3}{50}xx$$

\frac{29}{66} va \frac{99}{66} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{11}{8}\times \frac{29+99}{66}=\frac{3}{50}xx$$

128 olish uchun 29 va 99'ni qo'shing.

$$\frac{11}{8}\times \frac{128}{66}=\frac{3}{50}xx$$

\frac{128}{66} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{11}{8}\times \frac{64}{33}=\frac{3}{50}xx$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{11}{8} ni \frac{64}{33} ga ko‘paytiring.

$$\frac{11\times 64}{8\times 33}=\frac{3}{50}xx$$

\frac{11\times 64}{8\times 33} kasridagi ko‘paytirishlarni bajaring.

$$\frac{704}{264}=\frac{3}{50}xx$$

\frac{704}{264} ulushini 88 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{8}{3}=\frac{3}{50}xx$$

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

$$\frac{8}{3}=\frac{3}{50}x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{3}{50}x^{2}=\frac{8}{3}$$

Ikkala tarafdan \frac{8}{3} ni ayirish.

$$\frac{3}{50}x^{2}-\frac{8}{3}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{3}{50} ni a, 0 ni b va -\frac{8}{3} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{50}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{3}{50}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

-4 ni \frac{3}{50} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{6}{25}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali -\frac{6}{25} ni -\frac{8}{3} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$x=\frac{0±\sqrt{\frac{16}{25}}}{2\times \frac{3}{50}}$$

\frac{16}{25} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{4}{5}}{2\times \frac{3}{50}}$$

2 ni \frac{3}{50} marotabaga ko'paytirish.

$$x=\frac{0±\frac{4}{5}}{\frac{3}{25}}$$

x=\frac{0±\frac{4}{5}}{\frac{3}{25}} tenglamasini yeching, bunda ± musbat.

$$x=\frac{20}{3}$$

x=\frac{0±\frac{4}{5}}{\frac{3}{25}} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{20}{3}$$

Tenglama yechildi.

$$x=\frac{20}{3} x=-\frac{20}{3}$$