-x2-y3-%3D0-answer.jpeg "(x2 + Y2-1) X2 Y3 =0 Answer")
Solving the Equation (x2 + y2 - 1) x2 y3 = 0
In this article, we will explore the solution to the equation (x2 + y2 - 1) x2 y3 = 0. This equation involves a combination of quadratic and cubic terms, making it a bit more challenging to solve. However, with the right approach, we can find the solutions to this equation.
Factorization
The first step in solving this equation is to factorize the left-hand side of the equation. We can rewrite the equation as:
(x2 + y2 - 1) x2 y3 = 0
Factoring out the greatest common factor (GCF) of x2 and y3, we get:
x2 (x2 + y2 - 1) y3 = 0
This tells us that either x2 = 0 or (x2 + y2 - 1) y3 = 0.
Case 1: x2 = 0
If x2 = 0, then x = 0. This is a trivial solution to the equation.
Case 2: (x2 + y2 - 1) y3 = 0
If (x2 + y2 - 1) y3 = 0, then either (x2 + y2 - 1) = 0 or y3 = 0.
Subcase 2.1: (x2 + y2 - 1) = 0
Solving for x and y, we get:
x2 + y2 - 1 = 0
x2 + y2 = 1
This is a circle centered at the origin with a radius of 1.
Subcase 2.2: y3 = 0
If y3 = 0, then y = 0. This solution is valid for all values of x.
Conclusion
In conclusion, the solutions to the equation (x2 + y2 - 1) x2 y3 = 0 are:
x = 0x2 + y2 - 1 = 0(a circle centered at the origin with a radius of 1)y = 0(for all values ofx)
These solutions can be used to solve problems in various fields, such as physics, engineering, and computer science.
