In the following two equations numbered (I) and (II), solve both and determine the correct relationship between *x* and *y*.

I. $$x^2 - 8x + 15 = 0$$

II. $$2y^2 - 7y + 5 = 0$$

Question

In the following two equations numbered (I) and (II), solve both and determine the correct relationship between *x* and *y*.

I. $$x^2 - 8x + 15 = 0$$

II. $$2y^2 - 7y + 5 = 0$$

Accepted Answer

**Solution:**

1. Solve equation (I):
   $$x^2 - 8x + 15 = 0$$

Factorize:
   $$x^2 - 3x - 5x + 15 = 0$$
   $$ (x - 3)(x - 5) = 0 $$

So, the roots are:
   $$x = 3 	ext{ or } 5$$

2. Solve equation (II):
   $$2y^2 - 7y + 5 = 0$$

Factorize:
   $$2y^2 - 2y - 5y + 5 = 0$$
   $$ (2y - 5)(y - 1) = 0 $$

So, the roots are:
   $$y = \frac{5}{2} = 2.5 	ext{ or } 1$$

3. Compare the roots:
   - The maximum value of *x* is 5
   - The maximum value of *y* is 2.5

Since the largest root of *x* (5) is greater than the largest root of *y* (2.5), we conclude:

$$x > y$$

**Answer:** (a) $$x > y$$

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