(x-1)^2+(x-2)^2x-3)^2=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x-1)² + (x-2)² (x-3)² = 0

This equation presents a unique challenge, as it involves multiple squared terms. Here's how to solve it:

Understanding the Properties

• Squares are always non-negative: Any real number squared is greater than or equal to zero.
• Sum of non-negative terms: If the sum of several non-negative terms equals zero, each of those terms must be zero.

Applying the Properties to Solve

1. Analyze the Equation: We have three squared terms: (x-1)², (x-2)², and (x-3)². Each of these terms must be greater than or equal to zero.

2. Zero Sum Condition: The equation states that the sum of these three squared terms is equal to zero. Therefore, each term must be individually equal to zero.

3. Solve for x:

   • (x-1)² = 0 => x - 1 = 0 => x = 1
   • (x-2)² = 0 => x - 2 = 0 => x = 2
   • (x-3)² = 0 => x - 3 = 0 => x = 3

Conclusion:

The equation (x-1)² + (x-2)² (x-3)² = 0 has three solutions: x = 1, x = 2, and x = 3.