Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are given the equation $f(x) - g(x) = 3ax^2 + 2(a+1)x + a + 1$. We are also given that $a = \fra...
Quadratic EquationsParabolasIntersection of CurvesSystems of Equations
2025/6/10
Given that $f(x) - g(x) = 3ax^2 + 2(a+1)x + a+1$, we need to find the range of values for $a$ such t...
Quadratic InequalitiesQuadratic EquationsDiscriminantParabolasIntersection Points
2025/6/10
The problem is a fill-in-the-blank question. Given that for all real numbers $x$, $f(x) > g(x)$, det...
InequalitiesQuadratic FunctionsIntersection of CurvesProblem Solving
2025/6/10
The problem gives two quadratic functions $f(x) = 2ax^2 + (2a+1)x + a$ and $g(x) = -ax^2 - x - 1$. (...
Quadratic EquationsDiscriminantInequalitiesParabolas
2025/6/10
We are given a quadratic equation to solve: $x^2 - 6x + 9 = 0$. We need to find the value(s) of $x$ ...
Quadratic EquationsFactoringRoots of Equations
2025/6/10
We are given a sequence of numbers: $1, \frac{2}{2^{2-1}}, \frac{3}{3^{2-2}}, \frac{4}{4^{2-3}}, ......
SequencesSeriesExponentsGeneral Term
2025/6/10
The problem asks us to simplify the expression $\frac{2x-1}{3} - \frac{x-4}{4} + \frac{2x+1}{8}$ and...
Algebraic ManipulationSimplificationRational Expressions
2025/6/10
Solve for $x$ in the equation $(\frac{1}{4})^x = 8^{3x-2}$.
ExponentsEquationsSolving EquationsAlgebraic Manipulation
2025/6/10
The problem has two parts. (a) Expand and simplify the expression $(n+4)^2 + (n-2)^2$. (b) At an ele...
Expanding ExpressionsSimplifying ExpressionsSet TheoryVenn Diagrams
2025/6/10
The image presents several math problems. We will solve them one by one. The problems are: 1. a) Exp...
Expanding ExpressionsSimplifying ExpressionsVenn DiagramsLinear EquationsExponentsEquation SolvingKinematicsTrigonometrySimplifying Fractions
2025/6/10