Given the two equations:

(I) $ x - sqrt{169} = 0 $

(II) $ y^2 - 169 = 0 $

Find the correct relationship between $x$ and $y$.

Question

Given the two equations:

(I) $ x - sqrt{169} = 0 $

(II) $ y^2 - 169 = 0 $

Find the correct relationship between $x$ and $y$.

Accepted Answer

**Solution:**

1. Analyze equation (I):
   $$
   x - \sqrt{169} = 0 \implies x = \sqrt{169}
   $$
   Since $ \sqrt{169} = 13 $, we have:
   $$
   x = 13
   $$

2. Analyze equation (II):
   $$
   y^2 - 169 = 0 \implies y^2 = 169
   $$
   Taking square root on both sides:
   $$
   y = \pm \sqrt{169} = \pm 13
   $$

3. Possible values:
   - $ x = 13 $
   - $ y = 13 $ or $ y = -13 $

4. Compare $x$ and $y$:
   - If $ y = 13 $, then $ x = y $
   - If $ y = -13 $, then $ x > y $

5. Since $y$ can take two values, one equal to $x$ and one less than $x$, the exact relationship between $x$ and $y$ cannot be established uniquely.

**Answer:** x = y or relationship cannot be established

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