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

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

Baholash

$$\frac{\left(3x^{2}-1\right)^{2}}{9}$$

Qisqa yechim qadamlari

\frac{2x}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

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

\frac{2x\sqrt{3}}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\frac{2x}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

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

\frac{2x\sqrt{3}}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(x^{2}+\frac{2x\sqrt{3}+1}{3}\right)^{2} hosil qilish uchun x^{2}+\frac{2x\sqrt{3}+1}{3} va x^{2}+\frac{2x\sqrt{3}+1}{3} ni ko'paytirish.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{2} ni \frac{3}{3} marotabaga ko'paytirish.

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

\frac{3x^{2}}{3} va \frac{2x\sqrt{3}+1}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\frac{3x^{2}+2x\sqrt{3}+1}{3}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

3x^{2}+2x\sqrt{3}+1 kvadratini chiqarish.

$$\frac{9x^{4}+12\sqrt{3}x^{3}+4\left(\sqrt{3}\right)^{2}x^{2}+6x^{2}+4\sqrt{3}x+1}{3^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{9x^{4}+12\sqrt{3}x^{3}+4\times 3x^{2}+6x^{2}+4\sqrt{3}x+1}{3^{2}}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\frac{9x^{4}+12\sqrt{3}x^{3}+12x^{2}+6x^{2}+4\sqrt{3}x+1}{3^{2}}$$

18x^{2} ni olish uchun 12x^{2} va 6x^{2} ni birlashtirish.

$$\frac{9x^{4}+12\sqrt{3}x^{3}+18x^{2}+4\sqrt{3}x+1}{3^{2}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{9x^{4}+12\sqrt{3}x^{3}+18x^{2}+4\sqrt{3}x+1}{9}$$

Omil

$$\frac{\left(3x^{2}-1\right)^{2}}{9}$$