Author: aXa

Solving a System of Two Linear Equations

Solve the system of equations ax + by = m and cx + dy = n.

Solve for y in a system of two linear equations in two variables, where one equation contains a quadratic term

One of the equations is a system of two linear equations containing quadratic terms: ax² + by² + cx + dy = m, fx + gy = n. Can you solve for y in just one of the equations?

Formula 1 for Generating Relatively Prime Numbers

It tends to be a prime number relatively easily. There is a limit to 50 digits.

Solving quadratic equations

Let's solve the quadratic equation. If x and y are equal, it is a repeated root.

Formula 2 for Generating Relatively Prime Numbers

Generally, one of them will be a prime number. Depending on the value of a, the number of answers increases exponentially.

The value of x when the limit of a cubic function is considered

Find the value of x for which the limit of the cubic function f(x) = ax³ + bx² + cx + d holds. d cancels out during differentiation.

Find Pythagorean triples containing a single odd number (Can this be applied to complex numbers…?)

Substituting an even number works, but the answer is not an integer. Possible application to complex numbers (?) (The author did not create this with that in mind.)