Question

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

I. 3x² – 22x + 7 = 0

II. y² – 15y + 56 = 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

I. 3x2 – 22x + 7 = 0

⇒ 3x² – x – 21x + 7  0

⇒ x (3x – 1) –7 (3x – 1) = 0

⇒ (x – 7) (3x – 1) = 0

⇒ x = 7 or 1/3

II. y2 – 15y + 56 = 0 

⇒ y² – 8y – 7y + 56 = 0

⇒ y (y – 8) –7 (y –8) = 0

⇒ (y – 7) (y – 8) = 0

⇒ y = 7 or 8

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
7	7	x = y
7	8	x < y
1/3	7	x < y
1/3	8	x < y

∴ Clearly x ≤ y