GRE Math Domain 2: Algebra

If \( x \) and \( y \) are integers such that \( x^2 + y^2 = 100 \), what is the maximum possible value of \( x + y \)?

Solve for \( x \) in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).

If \( a \) and \( b \) are real numbers such that \( (a+bi)^2 = -16 + 30i \), what is the value of \( a^2 + b^2 \)?

Find the roots of the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

What is the solution to the system of equations \( 2x + 3y = 10 \) and \( 4x - y = -2 \)?

If \( 3^{2x-1} = 27 \), what is the value of \( x \)?

Given \( f(x) = x^2 - 4x + 4 \), for what value of \( x \) is \( f(x) = 0 \)?

If the sum of the roots of the quadratic equation \( ax^2 + bx + c = 0 \) is equal to its product of roots, which of the following is true?

Solve the inequality \( 2(x - 3) > 3(x + 1) \).

If \( (2x - 1)(x + 3) = 0 \), what are the possible values of \( x \)?

If \( \frac{1}{x-1} + \frac{1}{x+1} = \frac{2}{x} \), what is the value of \( x \)?

Given a quadratic equation \( x^2 + kx + 16 = 0 \), where \( k \) is a constant. If the equation has two distinct real roots, which of the following must be true?

The expression \( \frac{x^2 - 4}{x^2 - 2x - 3} \) can be simplified to:

If \( 5^{2x-1} = 125 \), what is the value of \( x \)?

What are the solutions to the equation \( x^2 - 5x + 6 = 0 \)?

The sum of a number and its reciprocal is 10/3. What is the number?

If \( x \) and \( y \) satisfy the equation \( 3x - 2y = 6 \), which of the following represents \( y \) in terms of \( x \)?

What is the coefficient of \( x \) in the expansion of \( (2x - 3)^4 \)?

If \( 2x + 3y = 12 \) and \( 3x + 2y = 12 \), what is the value of \( x - y \)?

For what values of \( x \) is the inequality \( \frac{x + 1}{x - 2} < 0 \) true?