Question

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

I. x2 – 21x + 108 = 0

II. y2 – 21y + 68 = 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 5 : x = y or relationship between x and y cannot be established.

Calculations:

I. x2 – 21x + 108 = 0

⇒ x2 – 12x – 9x + 108 = 0

⇒ x(x – 12) – 9(x – 12) = 0

⇒ (x – 12)(x – 9) = 0

⇒ x = 12, 9

II. y2 – 21y + 68 = 0

⇒ y2 – 17y – 4y + 68 = 0

⇒ y(y – 17) – 4(y – 17) = 0

⇒ (y – 17)(y – 4) = 0

⇒ y = 17, 4

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
12	17	x < y
12	4	x > y
9	17	x < y
9	4	x > y

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