Question

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² + 20x + 36 =0

II. y² – 20y + 51 = 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

Answer 1

Correct Answer - Option 3 :

x < y

Calculation:

I. x2 + 20x + 36 =0

⇒ x2 + 18x + 2x + 36 = 0

⇒ x(x + 18) + 2(x + 18) =0

⇒ (x + 18) (x + 2)

⇒ x = –18, –2

II. y2 – 20y + 51 = 0 

⇒ y2 – 17y – 3y + 51 = 0

⇒ y(y – 17) – 3(y – 17) = 0

⇒ (y – 17) (y – 3) = 0

⇒ y = 17, 3

Comparison between x and y (via tabulation):

X	Y	Relation
–18	17	x < y
–18	3	x < y
–2	17	x < y
–2	3	x < y

 

∴ x < y