New posts in algebra-precalculus

How to check if a sphere is fully inside another sphere

Sum of first n natural numbers proof

Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?

Finding out whether two line segments intersect each other

Calculate a quartic monic polynomial given that $P(1)=10,P(2)=20$ and $P(3)=30$.

Proving that $\sqrt{1 + x^2}$ is not a polynomial function

Finding $x^8+y^8+z^8$, given $x+y+z=0$, $\;xy +xz+yz=-1$, $\;xyz=-1$

Finding :$x_1^8+x_2^8+\cdots+x_8^8$

If $K = \frac{2}{1}\times \frac{4}{3}\times \cdots \times \frac{100}{99}.$ Then value of $\lfloor K \rfloor$

How to find the sum of this infinite series: $\sum_{n=1}^{ \infty } \frac1n \cdot \frac{H_{n+2}}{n+2}$ [closed]

Is there a general method to operate the reduction of a rational expression to a sum : $\frac {1+2x}{1-3x} \rightarrow 1+5x+\frac{15x^3}{1-3x}$

A general formula for $\sum (k-1)(k-2)(k-3)$?

How to know that $a^3+b^3 = (a+b)(a^2-ab+b^2)$

Can a cubic equation have three complex roots?

Monic polynomial of degree 5

Why isn't this approach in solving $x^2+x+1=0$ valid?

let $f(x) = (x-1)\ln x$, and given $0 < a < b$. If $f(a) = f(b)$, prove that $\frac{1}{\ln a}+\frac{1}{\ln b} < \frac{1}{2}$

Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$

Express product of a trigonometric function as a sum or difference

Inverse of a composite function