[(1/2)^4+(1/2)^2]-3[(1/sqrt{2})^2-1]-(frac{sqrt{3}}{2}) eching

$$[ ( \frac { 1 } { 2 } ) ^ { 4 } + ( \frac { 1 } { 2 } ) ^ { 2 } ] - 3 [ ( \frac { 1 } { \sqrt { 2 } } ) ^ { 2 } - 1 ] - ( \frac { \sqrt { 3 } } { 2 } )$$

Baholash

$$-\frac{\sqrt{3}}{2}+\frac{29}{16}\approx 0,946474596$$

Qisqa yechim qadamlari

4 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{16} ni qiymatni oling.

$$\frac{1}{16}+\left(\frac{1}{2}\right)^{2}-3\left(\left(\frac{1}{\sqrt{2}}\right)^{2}-1\right)-\frac{\sqrt{3}}{2}$$

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

$$\frac{1}{16}+\frac{1}{4}-3\left(\left(\frac{1}{\sqrt{2}}\right)^{2}-1\right)-\frac{\sqrt{3}}{2}$$

\frac{5}{16} olish uchun \frac{1}{16} va \frac{1}{4}'ni qo'shing.

$$\frac{5}{16}-3\left(\left(\frac{1}{\sqrt{2}}\right)^{2}-1\right)-\frac{\sqrt{3}}{2}$$

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{5}{16}-3\left(\left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}-1\right)-\frac{\sqrt{3}}{2}$$

\sqrt{2} kvadrati – 2.

$$\frac{5}{16}-3\left(\left(\frac{\sqrt{2}}{2}\right)^{2}-1\right)-\frac{\sqrt{3}}{2}$$

\frac{\sqrt{2}}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{5}{16}-3\left(\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}-1\right)-\frac{\sqrt{3}}{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{2^{2}}{2^{2}} marotabaga ko'paytirish.

$$\frac{5}{16}-3\left(\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}-\frac{2^{2}}{2^{2}}\right)-\frac{\sqrt{3}}{2}$$

\frac{\left(\sqrt{2}\right)^{2}}{2^{2}} va \frac{2^{2}}{2^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5}{16}-3\times \frac{\left(\sqrt{2}\right)^{2}-2^{2}}{2^{2}}-\frac{\sqrt{3}}{2}$$

3\times \frac{\left(\sqrt{2}\right)^{2}-2^{2}}{2^{2}} ni yagona kasrga aylantiring.

$$\frac{5}{16}-\frac{3\left(\left(\sqrt{2}\right)^{2}-2^{2}\right)}{2^{2}}-\frac{\sqrt{3}}{2}$$

\sqrt{2} kvadrati – 2.

$$\frac{5}{16}-\frac{3\left(2-2^{2}\right)}{2^{2}}-\frac{\sqrt{3}}{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{5}{16}-\frac{3\left(2-4\right)}{2^{2}}-\frac{\sqrt{3}}{2}$$

-2 olish uchun 2 dan 4 ni ayirish.

$$\frac{5}{16}-\frac{3\left(-2\right)}{2^{2}}-\frac{\sqrt{3}}{2}$$

-6 hosil qilish uchun 3 va -2 ni ko'paytirish.

$$\frac{5}{16}-\frac{-6}{2^{2}}-\frac{\sqrt{3}}{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{5}{16}-\frac{-6}{4}-\frac{\sqrt{3}}{2}$$

\frac{-6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{5}{16}-\left(-\frac{3}{2}\right)-\frac{\sqrt{3}}{2}$$

-\frac{3}{2} ning teskarisi \frac{3}{2} ga teng.

$$\frac{5}{16}+\frac{3}{2}-\frac{\sqrt{3}}{2}$$

\frac{29}{16} olish uchun \frac{5}{16} va \frac{3}{2}'ni qo'shing.

$$\frac{29}{16}-\frac{\sqrt{3}}{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 16 va 2 ning eng kichik umumiy karralisi 16. \frac{\sqrt{3}}{2} ni \frac{8}{8} marotabaga ko'paytirish.

$$\frac{29}{16}-\frac{8\sqrt{3}}{16}$$

\frac{29}{16} va \frac{8\sqrt{3}}{16} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{29-8\sqrt{3}}{16}$$

Omil

$$\frac{29 - 8 \sqrt{3}}{16} = 0,9464745962155614$$