-x2-y3-%3D0.jpeg "(x2+y2-1) X2 Y3 =0")
The Equation (x2 + y2 - 1) x2 y3 = 0: Understanding and Solving
The equation (x2 + y2 - 1) x2 y3 = 0 is a complex algebraic expression that involves the variables x and y. In this article, we will delve into the properties and characteristics of this equation, and explore methods for solving it.
Properties of the Equation
Non-Linear Equation
The equation (x2 + y2 - 1) x2 y3 = 0 is a non-linear equation, meaning that it does not have a constant degree of variables. The variables x and y are raised to different powers, making it challenging to solve using traditional linear methods.
Product of Factors
The equation can be rewritten as a product of two factors: (x2 + y2 - 1) and x2 y3. This suggests that the equation can be solved by finding the values of x and y that make each factor equal to zero.
Solving the Equation
Factoring the First Term
The first term, x2 + y2 - 1, can be factored as (x2 - 1) + y2. This allows us to rewrite the equation as ((x2 - 1) + y2) x2 y3 = 0.
Solving for x
Let's start by solving for x. Setting x2 - 1 = 0, we get x = ±1. Substituting these values back into the original equation, we get:
- For x = 1: (1 + y2 - 1) y3 = 0, which simplifies to y3 = 0, giving us y = 0.
- For x = -1: ((-1)2 - 1 + y2) y3 = 0, which simplifies to y3 = 0, giving us y = 0.
Solving for y
Now, let's solve for y. Setting y2 = 0, we get y = 0.
Conclusion
The equation (x2 + y2 - 1) x2 y3 = 0 has two solutions: x = ±1 and y = 0. These solutions can be obtained by factoring the equation and solving for each variable separately. Understanding the properties and characteristics of this equation can help us develop strategies for solving similar complex algebraic expressions.
