Solving the Equation 3x² + 3y × 4y = 0
The equation 3x² + 3y × 4y = 0 can be simplified and solved as follows:
- Simplify the equation:
3y × 4y = 12y², so the equation becomes:
3x² + 12y² = 0 - Factor out the common factor:
3(x² + 4y²) = 0 - Solve for the variables:
Since 3 ≠ 0, we must have:
x² + 4y² = 0 - Analyze the solution:
For real numbers x and y, both x² ≥ 0 and 4y² ≥ 0. The sum x² + 4y² can only equal zero if both terms are zero simultaneously:
x² = 0 AND 4y² = 0
Therefore: x = 0 AND y = 0
Final Solution: The only real solution to the equation is x = 0, y = 0.