Correct Answer - Option 3 : x ≤ y
Given:
I. x2 – 23x + 90 = 0
II. y2 – 37y + 342 = 0
Calculation:
I. x2 – 23x + 90 = 0
⇒ x2 - 18x - 5x + 90 = 0
⇒ x(x - 18) - 5(x - 18) = 0
⇒ (x - 18)(x - 5) = 0
⇒ x = 18, 5
II. y2 – 37y + 342 = 0
⇒ y2 - 18y - 19y + 342 = 0
⇒ y(y - 18) - 19(y - 18) = 0
⇒ (y - 18)(y - 19) = 0
⇒ y = 18, 19
Value of ‘x’
|
Relation
|
Value of ‘y’
|
18
|
=
|
18
|
18
|
<
|
19
|
5
|
<
|
18
|
5
|
<
|
19
|
When we compared the values of ‘x’ and ‘y’ in the table above, we found that there are 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.