Solving the Equation x2y - 4 0: Methods and Solutions

Ever wondered how to find the solutions to the equation x2y - 4 0? This article delves into the methods and steps required to solve the equation x2y - 4 0, discussing both theoretical and practical approaches. We will look at how to find the roots and explore the different values of x and y that satisfy the equation.

Step 1: Isolating y

The first approach to solving the equation involves isolating y. The given equation is x2y - 4 0. Let's begin by moving -4 to the other side:

x2y 4

Now, to isolate y, divide both sides by x2:

y 4 / x2

Step 2: Simplifying the Radical Form

Alternatively, you can take the square root of both sides to simplify the equation:

√x2y √4

Since √4 ± 2, the equation becomes:

√x2y ± 2

However, since x2 ≥ 0, √x2 |x|. Therefore:

√x2 |y| 2

Or:

|y| 2 / |x|

This suggests:

y ± 2 / |x|

Step 3: Exploring Integer Solutions

Another method, especially when dealing with specific values, involves hit and trial. Let's test some integer values for x to find corresponding values of y that satisfy the equation:

If x 0: 02 y - 4 0 > y 4 / 0 (Not valid, since division by zero is undefined) If x 1: 12 y - 4 0 > y 4 / 12 > y 4 If x 2: 22 y - 4 0 > 4y 4 > y 1 If x 4: 42 y - 4 0 > 16y 4 > y 1/4

The pattern shows that there are infinite number of pairs (x, y) that satisfy the equation. Some examples follow:

x 0, y undefined (Invalid) x 1, y 4 x 2, y 1 x 4, y 0.25 x 8, y 1/16

Conclusion

In summary, the equation x2y - 4 0 can be approached both theoretically and practically. The theoretical methods involve isolating variables and simplifying expressions, while the practical approach, such as hit and trial, helps identify specific pairs of (x, y) that satisfy the equation.

For further exploration, this equation highlights the infinite possibilities in the realm of x2y. Whether you're a mathematician or a student, understanding such equations enhances your problem-solving skills and mathematical intuition.