Question

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

I. x² – 22x + 120 = 0

II. y² – 26y + 168 = 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 4 : x ≤ y

Calculations:

I. x2– 22x + 120 = 0

⇒ x2 – 10x – 12x + 120 = 0

⇒ x(x – 10) – 12(x – 10) = 0

⇒ (x – 10)(x – 12) = 0

⇒ x = 10, 12

II. y2 – 26y + 168 = 0

⇒ y2 – 12y – 14y + 168 = 0

⇒ y(y – 12) – 14(y – 12) = 0

⇒ (y – 12)(y – 14) = 0

⇒ y = 12, 14

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
10	12	x < y
10	14	x < y
12	12	x = y
12	14	x < y

∴ x ≤ y