Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are asked to solve three problems. First, we need to find the value of $\frac{6^{1/2}9^{1/4}}{216...
ExponentsLogarithmsEquationsAlgebraic ManipulationChange of BaseQuadratic EquationsFactoring
2025/3/19
The problem asks to find the value of the expression $\frac{6^{1/4} 294^{1/4}}{216^{1/4}}$.
ExponentsRadicalsSimplification
2025/3/19
The problem is to simplify the expression $(\frac{1}{x} - x)^3 + (x + \frac{1}{x})^3$, given that $x...
PolynomialsLogarithmsSimplificationExponentsAlgebraic Manipulation
2025/3/19
We are asked to simplify two expressions: (1) Given that $x$ is real and $x \ne 0$, simplify the exp...
Algebraic SimplificationLogarithmsExponentsPolynomials
2025/3/19
Given that $x$ is real and $x \neq 0$, simplify the expression $(x-\frac{1}{x})^3 + (x+\frac{1}{x})^...
Algebraic simplificationPolynomialsExpansionExponents
2025/3/19
A man wants to distribute money. He gives $\frac{2}{5}$ to his wife and divides the rest equally amo...
FractionsWord ProblemLinear EquationsRatio and Proportion
2025/3/19
Solve the system of equations: $x - y = -1$ $x^2 + y = 1$
Systems of EquationsSubstitutionQuadratic Equations
2025/3/19
We are asked to solve the system of equations: $x^2 + y^2 = 3$ $x^2 - 15 = y$
Systems of EquationsQuadratic EquationsComplex NumbersDiscriminant
2025/3/19
Solve the system of equations: $x^2 + y^2 = 3$ $x^2 - 18 = y$
Systems of EquationsQuadratic EquationsSubstitutionComplex Numbers
2025/3/19
Solve the system of equations: $x^2 + y^2 = 10$ $y - x = 2$
Systems of EquationsQuadratic EquationsSubstitutionSolutions
2025/3/19