New posts in algebra-precalculus

For positive real numbers $a,b$ prove that $\sqrt[3]{2(a+b)(\frac{1}{a}+\frac{1}{b})}\ge\sqrt[3]{\frac{a}{b}}+\sqrt[3]{\frac{b}{a}}$.

What is the reason behind the Pythagorean relation in a hyperbola?

Largest Triangular Number less than a Given Natural Number

Determining the number $N$

If $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ then $x^{2000}+\frac{1}{x^{2000}}= $?

Effect of adding a constant to both Numerator and Denominator

Solving $45x-3795x^3 +95634x^5 - \cdots + 945x^{41}-45x^{43}+x^{45} = N$?

Sum of fifth roots of roots of cubic.

Algebraic equation problem - finding $x$

Find all positive integers $a, b, c$ such that $21^a+ 28^b= 35^c$ .

Find the Maximum Trigonometric polynomial coefficient $A_{k}$

Test to determine if a polynomial has only real roots?

$\left(\frac{a^2+d^2}{a+d}\right)^3+\left(\frac{b^2+c^2}{b+c}\right)^3\geq\left(\frac{a+b}{2}\right)^3+\left(\frac{c+d}{2}\right)^3$

Solving $ 1.2^x \le \log_{1.2} (x) $

Cyclic system of equations

Solving the functional equation $f(xy)=f(f(x)+f(y))$

Prove that there exists 3 numbers $a,b,c$ so that $P(a)=b, P(b)=c, P(c)=a$

A Detailed explanation for Archimedes area of parabolic segment by exhaustion proof ? Needed

Maximum value of $x$ such that $3^x-2^n$ is a prime.

UPDATED: If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, prove that $f(0) = 0.$