(x-frac{3-sqrt{5}}{2})(x-frac{sqrt{5}+3}{2} eching

$$( x - \frac { 3 - \sqrt { 5 } } { 2 } ) ( x - \frac { \sqrt { 5 } + 3 } { 2 }$$

Baholash

$$x^{2}-3x+1$$

Qisqa yechim qadamlari

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

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

\frac{2x}{2} va \frac{3-\sqrt{5}}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

2x-\left(3-\sqrt{5}\right) ichidagi ko‘paytirishlarni bajaring.

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

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

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

\frac{2x}{2} va \frac{\sqrt{5}+3}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2x-3+\sqrt{5}}{2}\times \frac{2x-\left(\sqrt{5}+3\right)}{2}$$

2x-\left(\sqrt{5}+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2x-3+\sqrt{5}}{2}\times \frac{2x-\sqrt{5}-3}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2x-3+\sqrt{5}}{2} ni \frac{2x-\sqrt{5}-3}{2} ga ko‘paytiring.

$$\frac{\left(2x-3+\sqrt{5}\right)\left(2x-\sqrt{5}-3\right)}{2\times 2}$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$\frac{\left(2x-3+\sqrt{5}\right)\left(2x-\sqrt{5}-3\right)}{4}$$

2x-3+\sqrt{5} ifodaning har bir elementini 2x-\sqrt{5}-3 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{4x^{2}-2x\sqrt{5}-6x-6x+3\sqrt{5}+9+2\sqrt{5}x-\left(\sqrt{5}\right)^{2}-3\sqrt{5}}{4}$$

-12x ni olish uchun -6x va -6x ni birlashtirish.

$$\frac{4x^{2}-2x\sqrt{5}-12x+3\sqrt{5}+9+2\sqrt{5}x-\left(\sqrt{5}\right)^{2}-3\sqrt{5}}{4}$$

0 ni olish uchun -2x\sqrt{5} va 2\sqrt{5}x ni birlashtirish.

$$\frac{4x^{2}-12x+3\sqrt{5}+9-\left(\sqrt{5}\right)^{2}-3\sqrt{5}}{4}$$

\sqrt{5} kvadrati – 5.

$$\frac{4x^{2}-12x+3\sqrt{5}+9-5-3\sqrt{5}}{4}$$

4 olish uchun 9 dan 5 ni ayirish.

$$\frac{4x^{2}-12x+3\sqrt{5}+4-3\sqrt{5}}{4}$$

0 ni olish uchun 3\sqrt{5} va -3\sqrt{5} ni birlashtirish.

$$\frac{4x^{2}-12x+4}{4}$$

1-3x+x^{2} natijani olish uchun 4x^{2}-12x+4 ning har bir ifodasini 4 ga bo‘ling.

$$1-3x+x^{2}$$

Omil

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