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

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

Baholash

$$\frac{13}{6}\approx 2,166666667$$

Yechim qadamlari

\sqrt{3} kvadrati – 3.

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

\frac{\sqrt{3}}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

1 ni \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} ga bo'lish 1 ga k'paytirish \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} ga qaytarish.

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

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

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

\sqrt{3} kvadrati – 3.

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

\frac{8}{3} olish uchun \frac{4}{3} va \frac{4}{3}'ni qo'shing.

$$\frac{8}{3}-\left(\frac{1}{\sqrt{2}}\right)^{2}$$

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

$$\frac{8}{3}-\left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}$$

\sqrt{2} kvadrati – 2.

$$\frac{8}{3}-\left(\frac{\sqrt{2}}{2}\right)^{2}$$

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

$$\frac{8}{3}-\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{8}{3}-\frac{2}{2^{2}}$$

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

$$\frac{8}{3}-\frac{2}{4}$$

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

$$\frac{8}{3}-\frac{1}{2}$$

\frac{13}{6} olish uchun \frac{8}{3} dan \frac{1}{2} ni ayirish.

$$\frac{13}{6}$$

Omil

$$\frac{13}{2 \cdot 3} = 2\frac{1}{6} = 2,1666666666666665$$