In each of the following, two equations (I) and (II) are given. Solve the equations and determine the correct relationship between *x* and *y*.

I: $2x^2 + 10x + 12 = 0$

II: $y^2 + 10x + 25 = 0$

Question

In each of the following, two equations (I) and (II) are given. Solve the equations and determine the correct relationship between *x* and *y*.

I: $2x^2 + 10x + 12 = 0$

II: $y^2 + 10x + 25 = 0$

Accepted Answer

**Solution:**

1. Solve equation (I):
   $$2x^2 + 10x + 12 = 0$$
   Divide entire equation by 2:
   $$x^2 + 5x + 6 = 0$$

2. Factorize:
   $$(x + 2)(x + 3) = 0$$
   So, $x = -2$ or $x = -3$

3. Solve equation (II):
   $$y^2 + 10x + 25 = 0$$
   Note that $x$ is a variable from equation (I), but here it appears as a constant term in equation (II). This suggests a possible typo or that $x$ is a constant in equation (II). Assuming it is a typo and should be $y^2 + 10y + 25 = 0$ (to solve for $y$), proceed:

4. Solve corrected equation (II):
   $$y^2 + 10y + 25 = 0$$
   This is a perfect square:
   $$(y + 5)^2 = 0$$
   So, $y = -5$

5. Compare values:
   - Possible $x$ values: $-2$, $-3$
   - $y = -5$

6. Since $-2 > -5$ and $-3 > -5$, for all values of $x$ from equation (I), $x > y$.

**Answer:** If $x > y$

Answer

Answer

Answer

Answer