Question

Разложить на множители: Хв 6 степени+1

Answer 1

Выражение Хв 6 степени+1 можно представить в виде х⁶ + 1⁶.
Но по правилам разложения суммы одинаковых четных степеней не делятся ни на разность, ни на сумму этих чисел,
То есть х⁶ + 1⁶ нельзя разделить ни на х - 1  ни на х + 1.

Answer 2

I can help you with math problems. To factorize $$x^6+1$$, you can use the formula $$a^3+b^3=(a+b)(a^2-ab+b^2)$$ and the identity $$x^2+y^2+z^2-xy-yz-zx=(x-y)(y-z)(z-x)$$.

First, rewrite $$x^6+1$$ as $$(x^2)^3+(1)^3$$ and apply the formula:

$$(x^2)^3+(1)^3=(x^2+1)((x^2)^2-x^2+1)$$

Then, expand the second factor and use the identity:

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

Therefore, the final answer is:

$$x^6+1=(x^2+1)(x^2-\frac{\sqrt{3}}{2}x-\frac{1}{2})(x^2+\frac{\sqrt{3}}{2}x-\frac{1}{2})$$

You can also use online calculators to check your answer or get more examples. Here are some links that might be useful:

- [Online calculator for factoring numbers](https://ru.onlinemschool.com/math/assistance/number_theory/multiplier/) - [Online calculator for factoring polynomials](https://ru.symbolab.com/solver/factor-calculator) - [Example of factoring a quadratic trinomial](https://uchi.ru/otvety/questions/razlozhite-na-mnozhiteli-kvadratniy-trehchlen-6x-2-5x-1)