%5E2%2B(y-4)%5E2%2B(z-5)%5E2%3D0-then-find-x%2By%2Bz.jpeg "(x-3)^2+(y-4)^2+(z-5)^2=0 Then Find X+y+z")
Understanding the Equation and Finding x+y+z
The equation (x-3)^2 + (y-4)^2 + (z-5)^2 = 0 represents a very specific scenario in three-dimensional space. Let's break it down:
Understanding the Equation:
- Squares: Each term in the equation is squared, meaning it will always be a non-negative value (zero or positive).
- Sum: The terms are added together.
- Equality to Zero: The sum of these squared terms equals zero.
For the sum of squares to be zero, each individual term must be zero. This is because:
- If any term is positive, the sum will be positive.
- If any term is negative, the sum will be positive.
- The only way the sum can be zero is if all the terms are zero.
Solving for x, y, and z:
Therefore, we can set each term equal to zero and solve:
- (x - 3)^2 = 0 => x - 3 = 0 => x = 3
- (y - 4)^2 = 0 => y - 4 = 0 => y = 4
- (z - 5)^2 = 0 => z - 5 = 0 => z = 5
Calculating x + y + z:
Now that we know the values of x, y, and z, we can simply add them together:
x + y + z = 3 + 4 + 5 = 12
Conclusion:
The equation (x-3)^2 + (y-4)^2 + (z-5)^2 = 0 represents a single point in three-dimensional space with coordinates (3, 4, 5). Therefore, the sum of x, y, and z is 12.