Prove by direct method that for any real number x,y if x = y then `x^(2) = y^(2)`.

Explanation

To prove that for any real numbers \( x \) and \( y \), if \( x = y \), then \( x^2 = y^2 \), we can follow these steps:

### Step 1: Start with the assumption
Assume that \( x = y \).

### Step 2: Square both sides
Since we have \( x = y \), we can square both sides of the equation:
\[ x^2 = y^2 \]

### Step 3: Conclusion
Thus, we have shown that if \( x = y \), then \( x^2 = y^2 \).

This completes the proof.