x:(7/3*21/2-21)=sqrt{(5/3+4/3-frac{2}{6}):(frac{3}{6}+4-frac{1}{3})}:(frac{4}{5}+2) eching

$$x : ( \frac { 7 } { 3 } \cdot \frac { 21 } { 2 } - 21 ) = \sqrt { ( \frac { 5 } { 3 } + \frac { 4 } { 3 } - \frac { 2 } { 6 } ) : ( \frac { 3 } { 6 } + 4 - \frac { 1 } { 3 } ) } : ( \frac { 4 } { 5 } + 2 )$$

x uchun yechish

$$x=1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{3} ni \frac{21}{2} ga ko‘paytiring.

$$\frac{x}{\frac{7\times 21}{3\times 2}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

\frac{7\times 21}{3\times 2} kasridagi ko‘paytirishlarni bajaring.

$$\frac{x}{\frac{147}{6}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

\frac{147}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{x}{\frac{49}{2}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

21 ni \frac{42}{2} kasrga o‘giring.

$$\frac{x}{\frac{49}{2}-\frac{42}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

\frac{49}{2} va \frac{42}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x}{\frac{49-42}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

7 olish uchun 49 dan 42 ni ayirish.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

\frac{5}{3} va \frac{4}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{5+4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

9 olish uchun 5 va 4'ni qo'shing.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

3 ni olish uchun 9 ni 3 ga bo‘ling.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{3-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

\frac{2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{3-\frac{1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

3 ni \frac{9}{3} kasrga o‘giring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9}{3}-\frac{1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

\frac{9}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9-1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

8 olish uchun 9 dan 1 ni ayirish.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

\frac{3}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1}{2}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

4 ni \frac{8}{2} kasrga o‘giring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1}{2}+\frac{8}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

\frac{1}{2} va \frac{8}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1+8}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

9 olish uchun 1 va 8'ni qo'shing.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{9}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

2 va 3 ning eng kichik umumiy karralisi 6 ga teng. \frac{9}{2} va \frac{1}{3} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{27}{6}-\frac{2}{6}}}}{\frac{4}{5}+2}$$

\frac{27}{6} va \frac{2}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{27-2}{6}}}}{\frac{4}{5}+2}$$

25 olish uchun 27 dan 2 ni ayirish.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{25}{6}}}}{\frac{4}{5}+2}$$

\frac{8}{3} ni \frac{25}{6} ga bo'lish \frac{8}{3} ga k'paytirish \frac{25}{6} ga qaytarish.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{8}{3}\times \frac{6}{25}}}{\frac{4}{5}+2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{8}{3} ni \frac{6}{25} ga ko‘paytiring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{8\times 6}{3\times 25}}}{\frac{4}{5}+2}$$

\frac{8\times 6}{3\times 25} kasridagi ko‘paytirishlarni bajaring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{48}{75}}}{\frac{4}{5}+2}$$

\frac{48}{75} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{16}{25}}}{\frac{4}{5}+2}$$

\frac{16}{25} boʻlinmasining kvadrat ildizini \frac{\sqrt{16}}{\sqrt{25}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4}{5}+2}$$

2 ni \frac{10}{5} kasrga o‘giring.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4}{5}+\frac{10}{5}}$$

\frac{4}{5} va \frac{10}{5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4+10}{5}}$$

14 olish uchun 4 va 10'ni qo'shing.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{14}{5}}$$

\frac{4}{5} ni \frac{14}{5} ga bo'lish \frac{4}{5} ga k'paytirish \frac{14}{5} ga qaytarish.

$$\frac{x}{\frac{7}{2}}=\frac{4}{5}\times \frac{5}{14}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{5} ni \frac{5}{14} ga ko‘paytiring.

$$\frac{x}{\frac{7}{2}}=\frac{4\times 5}{5\times 14}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{x}{\frac{7}{2}}=\frac{4}{14}$$

\frac{4}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{x}{\frac{7}{2}}=\frac{2}{7}$$

Ikkala tarafini \frac{7}{2} ga ko‘paytiring.

$$x=\frac{2}{7}\times \frac{7}{2}$$

\frac{2}{7} va uning teskari kasrini \frac{7}{2} ni qisqartiring.

$$x=1$$