Given the equations:

I: $$x^2 - 20x + 91 = 0$$

II: $$y^2 - 28y + 195 = 0$$

Which of the following relations between *x* and *y* is correct?

Question

Given the equations:

I: $$x^2 - 20x + 91 = 0$$

II: $$y^2 - 28y + 195 = 0$$

Which of the following relations between *x* and *y* is correct?

Accepted Answer

**Solution:**

1. Solve the first quadratic equation:
   
   $$x^2 - 20x + 91 = 0$$

Factorizing:

$$x^2 - 7x - 13x + 91 = 0$$

$$x(x - 7) - 13(x - 7) = 0$$

$$(x - 7)(x - 13) = 0$$

So, $$x = 7 	ext{ or } 13$$

2. Solve the second quadratic equation:

$$y^2 - 28y + 195 = 0$$

Factorizing:

$$y^2 - 13y - 15y + 195 = 0$$

$$y(y - 13) - 15(y - 13) = 0$$

$$(y - 13)(y - 15) = 0$$

So, $$y = 13 	ext{ or } 15$$

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

- Minimum value of *x* is 7, maximum is 13
   - Minimum value of *y* is 13, maximum is 15

Since the largest value of *x* (13) equals the smallest value of *y* (13), and the smallest value of *x* (7) is less than the smallest *y* (13), it follows that:

$$x \leq y$$

**Answer:** $x \leq y$

Answer

Answer

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