Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks to find the value of $a^3 - \frac{1}{a^3}$ given that $a^4 - 27a^2 + 1 = 0$.
Polynomial EquationsAlgebraic ManipulationFactoringExponents
2025/4/24
The first problem (marked with "গ") asks to show something, given $a = 2 + \sqrt{3}$ and $a+b = 4$. ...
FactorizationDifference of SquaresAlgebraic Manipulation
2025/4/24
The problem has three parts. First, given $a = 2 + \sqrt{3}$ and $a + b = 4$, we need to solve part ...
Algebraic ManipulationSimplificationFactoringSurds
2025/4/24
The problem asks for the natural domain of the function $f(x, y) = \frac{y}{x} + xy$, and to evaluat...
FunctionsDomainFunction EvaluationAlgebraic Expressions
2025/4/24
The problem asks us to find the domain of the function $f(x, y) = \frac{y}{x} + xy$ and evaluate the...
FunctionsDomainFunction EvaluationExpressions
2025/4/24
The problem defines a function $f(x, y) = x^2 y + \sqrt{y}$. We are asked to evaluate this function ...
FunctionsFunction EvaluationExponentsSquare RootsAlgebraic Expressions
2025/4/24
The problem asks to solve the trigonometric inequality $2\sin^2\theta \ge 3\cos\theta$.
TrigonometryInequalitiesTrigonometric IdentitiesQuadratic Equations
2025/4/24
The problem is to simplify the expression $D = \sqrt{\frac{2}{1+sin\alpha} + \frac{2}{1-sin\alpha}}$...
TrigonometrySimplificationAlgebraic ManipulationTrigonometric IdentitiesSquare Roots
2025/4/24
The problem is to solve the equation $\sin(\theta - \frac{\pi}{3}) = -\frac{1}{2}$ for $0 \le \theta...
TrigonometryTrigonometric EquationsSine FunctionSolving Equations
2025/4/24
The problem gives the general term of a sequence $a_n = \frac{1}{n(n+1)}$, and asks us to find the s...
Sequences and SeriesPartial FractionsTelescoping Sum
2025/4/24