Given the two quadratic equations:

I. $$x^2 - 17x + 70 = 0$$

II. $$y^2 - 14y + 48 = 0$$

Compare the values of *x* and *y* based on the solutions of these equations and select the correct option.

Question

Given the two quadratic equations:

I. $$x^2 - 17x + 70 = 0$$

II. $$y^2 - 14y + 48 = 0$$

Compare the values of *x* and *y* based on the solutions of these equations and select the correct option.

Accepted Answer

**Solution:**

1. Solve the first quadratic equation:
   $$x^2 - 17x + 70 = 0$$

Factors of 70 that add up to 17 are 7 and 10.

So, $$x^2 - 17x + 70 = (x - 7)(x - 10) = 0$$

Therefore, $$x = 7$$ or $$x = 10$$.

2. Solve the second quadratic equation:
   $$y^2 - 14y + 48 = 0$$

Factors of 48 that add up to 14 are 6 and 8.

So, $$y^2 - 14y + 48 = (y - 6)(y - 8) = 0$$

Therefore, $$y = 6$$ or $$y = 8$$.

3. Now, compare the possible values of $$x$$ and $$y$$:
   - $$x$$ can be 7 or 10
   - $$y$$ can be 6 or 8

4. Possible comparisons:
   - If $$x = 7$$ and $$y = 8$$, then $$x < y$$.
   - If $$x = 7$$ and $$y = 6$$, then $$x > y$$.
   - If $$x = 10$$ and $$y = 6$$, then $$x > y$$.
   - If $$x = 10$$ and $$y = 8$$, then $$x > y$$.

5. Since $$x$$ and $$y$$ can be either greater or smaller than each other depending on the roots chosen, no definite relation can be established.

**Answer:** If $$x = y$$ or no relation can be established between $$x$$ and $$y$$.

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