Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks to find the maximum value $M$ of the function $f(x) = |x^2 - 2x|$ in the interval $...
FunctionsAbsolute ValueMaximum ValueOptimizationIntervals
2025/4/14
We are asked to expand the expression $(7 + \sqrt{3x})^2$.
Algebraic ExpansionSquare of a BinomialRadicals
2025/4/14
We are given the function $f(x) = |x-5| - 1$. We need to determine if the function is even, odd, or...
FunctionsAbsolute ValueEven/Odd FunctionsRange of a FunctionGraphing
2025/4/14
We are given two sequences $(U_n)_{n \in \mathbb{N}}$ and $(V_n)_{n \in \mathbb{N}}$ defined by the ...
SequencesSeriesGeometric SequencesConvergenceLimits
2025/4/14
We are given two sequences, $(U_n)_{n \in \mathbb{N}}$ and $(V_n)_{n \in \mathbb{N}}$, defined by $U...
SequencesGeometric SequencesRecurrence RelationsExplicit Formula
2025/4/14
We are given two expressions involving trigonometric functions: $cos^4x = \frac{1}{8}cos4x + \frac{1...
TrigonometryTrigonometric IdentitiesDouble-Angle Formulas
2025/4/14
We are given two exercises. Exercise 16: We are given the equation (E): $8x^3 - 4\sqrt{3}x^2 - 2x + ...
Polynomial EquationsTrigonometric EquationsTrigonometric IdentitiesSolving EquationsRoots of Equations
2025/4/14
We are given a system of equations (S): $x + y = \frac{\pi}{6}$ $sinx \cdot siny = -\frac{\sqrt{3}}{...
TrigonometrySystems of EquationsTrigonometric Identities
2025/4/14
The problem consists of four parts: 1. Verify the equality $\sqrt{3 + 2\sqrt{2}} = 1 + \sqrt{2}$.
RadicalsQuadratic EquationsQuadratic InequalitiesTrigonometryTrigonometric EquationsTrigonometric Inequalities
2025/4/14
Exercise 11: Find all real numbers $x$ and $y$ in the interval $[0, 2\pi)$ such that $\begin{cases} ...
TrigonometryEquationsTrigonometric IdentitiesQuadratic EquationsSolution Sets
2025/4/14