(1/2)^3+(1/3)^3-(5/6)^3 eching

$$( \frac { 1 } { 2 } ) ^ { 3 } + ( \frac { 1 } { 3 } ) ^ { 3 } - ( \frac { 5 } { 6 } ) ^ { 3 }$$

Baholash

$$-\frac{5}{12}\approx -0,416666667$$

Yechim qadamlari

3 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{8} ni qiymatni oling.

$$\frac{1}{8}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}$$

3 daraja ko‘rsatkichini \frac{1}{3} ga hisoblang va \frac{1}{27} ni qiymatni oling.

$$\frac{1}{8}+\frac{1}{27}-\left(\frac{5}{6}\right)^{3}$$

8 va 27 ning eng kichik umumiy karralisi 216 ga teng. \frac{1}{8} va \frac{1}{27} ni 216 maxraj bilan kasrlarga aylantirib oling.

$$\frac{27}{216}+\frac{8}{216}-\left(\frac{5}{6}\right)^{3}$$

\frac{27}{216} va \frac{8}{216} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{27+8}{216}-\left(\frac{5}{6}\right)^{3}$$

35 olish uchun 27 va 8'ni qo'shing.

$$\frac{35}{216}-\left(\frac{5}{6}\right)^{3}$$

3 daraja ko‘rsatkichini \frac{5}{6} ga hisoblang va \frac{125}{216} ni qiymatni oling.

$$\frac{35}{216}-\frac{125}{216}$$

\frac{35}{216} va \frac{125}{216} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{35-125}{216}$$

-90 olish uchun 35 dan 125 ni ayirish.

$$\frac{-90}{216}$$

\frac{-90}{216} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{5}{12}$$

Omil

$$-\frac{5}{12} = -0,4166666666666667$$