Correct Answer  Option 4 :
x ≥ y
Calculation:
I. x2 – 20x + 91 = 0
⇒ x^{2 }– 13x – 7x + 91 = 0
⇒ x(x – 13) – 7(x – 13)= 0
⇒ (x – 13)(x – 7) = 0
⇒ x = 13, 7
II. y2 + 6y – 91 = 0
⇒ y^{2 }+ 13y – 7y – 91 = 0
⇒ y(y + 13) – 7(y + 13) =0
⇒ (y + 13)(y – 7) = 0
⇒ y = 7, (13)
Value of ‘x’

Relation

Value of ‘y’

13

>

7

13

>

13

7

=

7

7

>

13

When we compared the values of ‘x’ and ‘y’ in the table above, we found that there is TWO relations between X and Y i.e. > and =. So, a relation between x and y is “x ≥ y”.
∴ After comparison, all the values of x and y the relation is “x ≥ y”.