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New posts in algebra-precalculus
For positive real numbers $a,b$ prove that $\sqrt[3]{2(a+b)(\frac{1}{a}+\frac{1}{b})}\ge\sqrt[3]{\frac{a}{b}}+\sqrt[3]{\frac{b}{a}}$.
algebra-precalculus
inequality
polynomials
means
a.m.-g.m.-inequality
What is the reason behind the Pythagorean relation in a hyperbola?
algebra-precalculus
analytic-geometry
conic-sections
Largest Triangular Number less than a Given Natural Number
real-analysis
algebra-precalculus
number-theory
Determining the number $N$
algebra-precalculus
number-theory
diophantine-equations
If $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ then $x^{2000}+\frac{1}{x^{2000}}= $?
algebra-precalculus
Effect of adding a constant to both Numerator and Denominator
algebra-precalculus
fractions
Solving $45x-3795x^3 +95634x^5 - \cdots + 945x^{41}-45x^{43}+x^{45} = N$?
algebra-precalculus
trigonometry
polynomials
Sum of fifth roots of roots of cubic.
algebra-precalculus
Algebraic equation problem - finding $x$
algebra-precalculus
polynomials
exponentiation
Find all positive integers $a, b, c$ such that $21^a+ 28^b= 35^c$ .
algebra-precalculus
diophantine-equations
exponential-sum
perfect-powers
Find the Maximum Trigonometric polynomial coefficient $A_{k}$
algebra-precalculus
trigonometry
inequality
trigonometric-series
Test to determine if a polynomial has only real roots?
complex-analysis
algebra-precalculus
algebraic-geometry
polynomials
roots
$\left(\frac{a^2+d^2}{a+d}\right)^3+\left(\frac{b^2+c^2}{b+c}\right)^3\geq\left(\frac{a+b}{2}\right)^3+\left(\frac{c+d}{2}\right)^3$
algebra-precalculus
inequality
contest-math
Solving $ 1.2^x \le \log_{1.2} (x) $
algebra-precalculus
logarithms
Cyclic system of equations
algebra-precalculus
contest-math
systems-of-equations
Solving the functional equation $f(xy)=f(f(x)+f(y))$
algebra-precalculus
functional-equations
Prove that there exists 3 numbers $a,b,c$ so that $P(a)=b, P(b)=c, P(c)=a$
algebra-precalculus
polynomials
lagrange-interpolation
A Detailed explanation for Archimedes area of parabolic segment by exhaustion proof ? Needed
calculus
sequences-and-series
algebra-precalculus
proof-explanation
area
Maximum value of $x$ such that $3^x-2^n$ is a prime.
algebra-precalculus
number-theory
elementary-number-theory
discrete-mathematics
prime-numbers
UPDATED: If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, prove that $f(0) = 0.$
algebra-precalculus
inequality
proof-writing
contest-math
solution-verification
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