Given the two equations:

(I) $ $x = \sqrt{289}$ $

(II) $ $y^2 = 289$ $

Determine the correct relationship between $x$ and $y$:

Question

Given the two equations:

(I) $ $x = \sqrt{289}$ $

(II) $ $y^2 = 289$ $

Determine the correct relationship between $x$ and $y$:

Accepted Answer

**Solution:**

1. From equation (I):
   $$ $x = \sqrt{289} = 17$ $$

2. From equation (II):
   $$ $y^2 = 289 \implies y = \pm 17$ $$

3. Since $y$ can be either $17$ or $-17$, we analyze both cases:
   - If $y = 17$, then $x = y$.
   - If $y = -17$, then $x = 17 > -17 = y$.

4. Therefore, in all cases, $$x \geq y$$.

**Answer:** (b) If $$x \geq y$$

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