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(3x-y)^2+(x-5)^2=0 Solve For X And Y

2 min read Jun 16, 2024
(3x-y)^2+(x-5)^2=0 Solve For X And Y

Solving the Equation (3x-y)^2 + (x-5)^2 = 0

This equation presents a unique situation that we can solve by utilizing the properties of squares and the concept of zero.

Understanding the Equation:

  • The equation is a sum of two squared terms, both set equal to zero.
  • Remember that any real number squared is always greater than or equal to zero.

Solving for x and y:

  1. Consider the Individual Terms: For the equation to be true, both terms on the left-hand side must be equal to zero.

  2. Solve for (3x - y)^2 = 0:

    • Taking the square root of both sides, we get: 3x - y = 0

  3. Solve for (x - 5)^2 = 0:

    • Taking the square root of both sides, we get: x - 5 = 0
    • Therefore, x = 5

  4. Substitute x back into the equation from step 2:

    • 3(5) - y = 0
    • 15 - y = 0
    • y = 15

Conclusion:

The solution to the equation (3x - y)^2 + (x - 5)^2 = 0 is x = 5 and y = 15. This is the only possible solution because the equation requires both squared terms to be zero simultaneously.

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