Question

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

I. x² – 27x + 162 = 0

II. y² + 6y – 135 = 0

1. x > y
2. x ≥ y
3. y > x
4. y ≥ x
5. x = y or relationship between x and y cannot be established.

Answer 1

Correct Answer - Option 2 : x ≥ y

According to given equations

I. x2 – 27x + 162 = 0

⇒ x2 – 18x – 9x + 162 = 0

⇒ x(x – 18) – 9(x – 18) = 0

⇒ (x – 18) (x – 9) = 0

⇒ x = 18, 9

II. y2 + 6y – 135 = 0

⇒ y2 + 15y – 9y – 135 = 0

⇒ y(y + 15) – 9(y + 15) = 0

⇒ (y + 15) (y – 9) = 0

⇒ y = 9, -15

Comparison between x and y (via Tabulation):

x	y	Relation
18	9	x>y
18	-15	x>y
9	9	x=y
9	-15	x>y

∴ x ≥ y