Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
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
The problem asks to simplify the expression $a + a$.
SimplificationAlgebraic ExpressionsCombining Like Terms
2025/4/14
The problem gives an equation $z = \sqrt{16 - x^2 - y^2}$. We are asked to solve the problem. The ...
FunctionsDomainRangeInequalitiesSquare Roots
2025/4/14
The problem has two parts: (a) involves linear transformations and matrices, and (b) involves polyno...
Linear TransformationsMatricesMatrix MultiplicationMatrix InversePolynomialsRemainder TheoremQuadratic Equations
2025/4/13
We are given a set of multiple-choice questions involving calculus concepts, likely for a calculus e...
ExponentsLogarithmsEquations
2025/4/13
Given that $(x+2)$ and $(2x+3)$ are factors of $f(x) = 6x^3 + px^2 + 4x - q$, we need to find the va...
PolynomialsFactor TheoremPolynomial DivisionRoots of PolynomialsCubic EquationsSystems of Equations
2025/4/13