A Good Example of Mathematical Writing

Always Begin with Definitions and Assumptions

The following is a given equation consisting of two variables x and y. 2y2 = 2x2 + 4x + 2 By dividing the both sides of the equation by 2, we have the following. y2 = x2 + 2x + 1 The right-hand side of the equation can be factorized as follows. x2 + 2x + 1 = (x + 1)2 Thus, the given equation is transformed as follows. y2 = (x + 1)2 This quadratic equation has two distinct solutions of y in terms of x: y = x + 1 and y = −(x + 1). Note that there are an infinite number of pairs of x and y that satisfy the given equation. Therefore, solutions of the given equation are all pairs of x and y that satisfy at least one of the two linear equations y = x + 1 and y = −(x + 1).