Given the two quadratic equations:

I. $$x^2 - 7x + 12 = 0$$

II. $$y^2 - 8y + 12 = 0$$

Solve both equations and determine the correct relationship between *x* and *y*.

Choose the correct option:

Question

Given the two quadratic equations:

I. $$x^2 - 7x + 12 = 0$$

II. $$y^2 - 8y + 12 = 0$$

Solve both equations and determine the correct relationship between *x* and *y*.

Choose the correct option:

Accepted Answer

**Solution:**

1. Solve equation I: $$x^2 - 7x + 12 = 0$$

- Factorize as: $$(x - 4)(x - 3) = 0$$
   - So, $$x = 4$$ or $$x = 3$$

2. Solve equation II: $$y^2 - 8y + 12 = 0$$

- Factorize as: $$(y - 6)(y - 2) = 0$$
   - So, $$y = 6$$ or $$y = 2$$

3. Now, compare possible values of *x* and *y*:

- *x* can be 3 or 4
   - *y* can be 2 or 6

4. Possible comparisons:

- When $$x = 3$$ and $$y = 6$$, then $$y > x$$
   - When $$x = 4$$ and $$y = 2$$, then $$x > y$$

Since the values of *x* and *y* vary such that no definite relation (like $$x > y$$ or $$y > x$$) always holds, we cannot establish a fixed relationship between *x* and *y*.

**Answer:** (e) If $$x = y$$ or no relation can be established

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