(1/4-3/2+1/20+1/5)^3-(-frac{1}{3}+1)^2+(frac{12}{5}-frac{3}{20}-frac{25}{12})^2 eching

$$( \frac { 1 } { 4 } - \frac { 3 } { 2 } + \frac { 1 } { 20 } + \frac { 1 } { 5 } ) ^ { 3 } - ( - \frac { 1 } { 3 } + 1 ) ^ { 2 } + ( \frac { 12 } { 5 } - \frac { 3 } { 20 } - \frac { 25 } { 12 } ) ^ { 2 }$$

Baholash

$$-\frac{17}{12}\approx -1,416666667$$

Yechim qadamlari

-\frac{5}{4} olish uchun \frac{1}{4} dan \frac{3}{2} ni ayirish.

$$\left(-\frac{5}{4}+\frac{1}{20}+\frac{1}{5}\right)^{3}-\left(-\frac{1}{3}+1\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

-\frac{6}{5} olish uchun -\frac{5}{4} va \frac{1}{20}'ni qo'shing.

$$\left(-\frac{6}{5}+\frac{1}{5}\right)^{3}-\left(-\frac{1}{3}+1\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

-1 olish uchun -\frac{6}{5} va \frac{1}{5}'ni qo'shing.

$$\left(-1\right)^{3}-\left(-\frac{1}{3}+1\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

3 daraja ko‘rsatkichini -1 ga hisoblang va -1 ni qiymatni oling.

$$-1-\left(-\frac{1}{3}+1\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

\frac{2}{3} olish uchun -\frac{1}{3} va 1'ni qo'shing.

$$-1-\left(\frac{2}{3}\right)^{2}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

2 daraja ko‘rsatkichini \frac{2}{3} ga hisoblang va \frac{4}{9} ni qiymatni oling.

$$-1-\frac{4}{9}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

-\frac{13}{9} olish uchun -1 dan \frac{4}{9} ni ayirish.

$$-\frac{13}{9}+\left(\frac{12}{5}-\frac{3}{20}-\frac{25}{12}\right)^{2}$$

\frac{9}{4} olish uchun \frac{12}{5} dan \frac{3}{20} ni ayirish.

$$-\frac{13}{9}+\left(\frac{9}{4}-\frac{25}{12}\right)^{2}$$

\frac{1}{6} olish uchun \frac{9}{4} dan \frac{25}{12} ni ayirish.

$$-\frac{13}{9}+\left(\frac{1}{6}\right)^{2}$$

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

$$-\frac{13}{9}+\frac{1}{36}$$

-\frac{17}{12} olish uchun -\frac{13}{9} va \frac{1}{36}'ni qo'shing.

$$-\frac{17}{12}$$

Omil

$$-\frac{17}{12} = -1\frac{5}{12} = -1,4166666666666667$$