1.

In the given question, two equations numbered l and II are given. Solve both the equations andmark the appropriate answer.I. x2 + 12x + 32 = 0 II. y2 + 6y + 8 = 01. x > y2. x < y3. x ≤ y4. x ≥ y5. x = y or the relationship between x and y cannot be established.

Answer» Correct Answer - Option 3 : x ≤ y

Calculation:

From I,

x2 + 12x + 32 = 0

⇒ x2 + 8x + 4x +32 = 0

⇒ x(x+8) + 4(x+8) = 0

⇒ (x+4) (x+8) = 0

Taking, 

⇒ x + 4 = 0 or x + 8 = 0

⇒ x = –4 or –8

From II, 

y2 + 6y + 8 = 0

⇒ y2 + 4y + 2y + 8 = 0

⇒ y(y+4) + 2(y+4) = 0 

⇒ (y+2) (y+4) = 0

Taking,

⇒ y + 2 = 0 or y + 4 = 0

⇒ y = –2 or –4

Comparison between x and y (via Tabulation):

Values of xValues of yRelation    
–4–2x < y
–4–4x = y
–8–2x < y
–8–4x < y

 

∴ Relation between x and y is, x ≤ y. 


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