x^6-1 eching

$${ x }^{ 6 } -1$$

Omil

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

Yechim qadamlari

x^{6}-1 ni \left(x^{3}\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Hisoblang: x^{3}-1. x^{3}-1 ni x^{3}-1^{3} sifatida qaytadan yozish. Kublarning farqini ushbu formula bilan hisoblash mumkin: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

Hisoblang: x^{3}+1. x^{3}+1 ni x^{3}+1^{3} sifatida qaytadan yozish. Kublar yigʻindisini ushbu formula bilan hisoblash mumkin: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

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

Toʻliq ajratilgan ifodani qaytadan yozing. Quyidagi koʻphadlar faktorlanmagan, ularda hech qanday ratsional ildizlar topilmadi: x^{2}-x+1,x^{2}+x+1.

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

Baholash

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