(1-1/2)^2(-2)^3-3/2+|-(-1/6)^2+frac{1/4-frac{1}{5}}{(1-frac{2}{5})^2}|-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}= eching

$$( 1 - \frac { 1 } { 2 } ) ^ { 2 } ( - 2 ) ^ { 3 } - \frac { 3 } { 2 } + | - ( - \frac { 1 } { 6 } ) ^ { 2 } + \frac { \frac { 1 } { 4 } - \frac { 1 } { 5 } } { ( 1 - \frac { 2 } { 5 } ) ^ { 2 } } | - \frac { \frac { 1 } { 3 } - \frac { 2 } { 9 } } { \frac { 1 } { 8 } - \frac { 15 } { 8 } } =$$

Baholash

$$-\frac{419}{126}\approx -3,325396825$$

Yechim qadamlari

\frac{1}{2} olish uchun 1 dan \frac{1}{2} ni ayirish.

$$\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

2 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{4} ni qiymatni oling.

$$\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

3 daraja ko‘rsatkichini -2 ga hisoblang va -8 ni qiymatni oling.

$$\frac{1}{4}\left(-8\right)-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-2 hosil qilish uchun \frac{1}{4} va -8 ni ko'paytirish.

$$-2-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-\frac{7}{2} olish uchun -2 dan \frac{3}{2} ni ayirish.

$$-\frac{7}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

2 daraja ko‘rsatkichini -\frac{1}{6} ga hisoblang va \frac{1}{36} ni qiymatni oling.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{1}{20} olish uchun \frac{1}{4} dan \frac{1}{5} ni ayirish.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{3}{5} olish uchun 1 dan \frac{2}{5} ni ayirish.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

2 daraja ko‘rsatkichini \frac{3}{5} ga hisoblang va \frac{9}{25} ni qiymatni oling.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{1}{20} ni \frac{9}{25} ga bo'lish \frac{1}{20} ga k'paytirish \frac{9}{25} ga qaytarish.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{1}{20}\times \frac{25}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{5}{36} hosil qilish uchun \frac{1}{20} va \frac{25}{9} ni ko'paytirish.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{5}{36}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{1}{9} olish uchun -\frac{1}{36} va \frac{5}{36}'ni qo'shing.

$$-\frac{7}{2}+|\frac{1}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

a haqiqiy sonining mutloq qiymati qachon a\geq 0 bo‘lganda, a yoki qachon a<0 bo‘lganda -a. \frac{1}{9} ning mutloq qiymati \frac{1}{9} ga teng.

$$-\frac{7}{2}+\frac{1}{9}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-\frac{61}{18} olish uchun -\frac{7}{2} va \frac{1}{9}'ni qo'shing.

$$-\frac{61}{18}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{1}{9} olish uchun \frac{1}{3} dan \frac{2}{9} ni ayirish.

$$-\frac{61}{18}-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-\frac{7}{4} olish uchun \frac{1}{8} dan \frac{15}{8} ni ayirish.

$$-\frac{61}{18}-\frac{\frac{1}{9}}{-\frac{7}{4}}$$

\frac{1}{9} ni -\frac{7}{4} ga bo'lish \frac{1}{9} ga k'paytirish -\frac{7}{4} ga qaytarish.

$$-\frac{61}{18}-\frac{1}{9}\left(-\frac{4}{7}\right)$$

-\frac{4}{63} hosil qilish uchun \frac{1}{9} va -\frac{4}{7} ni ko'paytirish.

$$-\frac{61}{18}-\left(-\frac{4}{63}\right)$$

-\frac{4}{63} ning teskarisi \frac{4}{63} ga teng.

$$-\frac{61}{18}+\frac{4}{63}$$

-\frac{419}{126} olish uchun -\frac{61}{18} va \frac{4}{63}'ni qo'shing.

$$-\frac{419}{126}$$

Omil

$$-\frac{419}{126} = -3\frac{41}{126} = -3,3253968253968256$$