Question

In the given questions, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.

l. x² – x – 132 = 0

II. y² – 31y + 210 = 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.

Calculation:

l. x2 – x  – 132 = 0

⇒ x2 – (12 – 11)x – 132 = 0

⇒ x2 – 12x + 11x – 132 = 0

⇒ x (x – 12) + 11 (x – 12) = 0

⇒ (x – 12) (x + 11) = 0

⇒ x = 12, –11

 

II. y2 – 31y + 210 = 0

⇒ y2 – (10 + 21)y + 210 = 0

⇒ y2 – 10y – 21y + 210 = 0

⇒ y (y – 10) – 21 (y – 10) = 0

⇒ (y – 21) (y – 10) = 0

⇒ y = 21, 10

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
12	21	x <y
12	10	x > y
-11	21	x < y
-11	10	x < y

 

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