# In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2 + 8x + 12 = 0II. y2 + 14y + 24 = 0

1. x > y

2. x ≥ y

3. x < y

4. x ≤ y

5. x = y or relationship between x and y cannot be established

Option 5 :

x = y or relationship between x and y cannot be established

## Detailed Solution

Calculation:

I. x2 + 8x + 12 = 0

⇒ x2 + 6x + 2x + 12 = 0

⇒ x(x + 6) + 2(x + 6) = 0

⇒ (x + 6) (x + 2) =0

⇒ x = –6, –2

II. y2 + 14y + 24 = 0

⇒ y2 + 12x + 2x + 24 = 0

⇒ y(y + 12) + 2(x + 12) = 0

⇒ (y + 12) (x + 2) = 0

⇒ y = –12, –2

Comparison between x and y (via tabulation):

 X Y Relation –6 –12 x > y –6 –2 x < y –2 –12 x > y –2 –2 x =y

∴ x = y or relationship between x and y cannot be established

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