Correct Answer - Option 5 : No relation in x and y or x = y
Calculation:
From I,
6x2 - 19x + 15 = 0
⇒ 6x2 - 10x - 9x + 15 = 0
⇒ 2x(3x - 5) - 3(3x - 5) = 0
⇒ (2x - 3)(3x - 5) = 0
Taking,
⇒ 2x - 3 = 0 or 3x - 5 = 0
⇒ x = 3/2 or x = 5/3
From II,
2y2 - 11y + 5 = 0
⇒ 2y2 - 10y - y + 5 = 0
⇒ 2y(y - 5) - 1(y - 5) = 0
⇒ (2y - 1)(y - 5) = 0
Taking,
⇒ 2y - 1 = 0 or y - 5 = 0
⇒ y = 1/2 or y = 5
Comparison between x and y (via Tabulation):
x
|
Y
|
Relation
|
3/2
|
1/2
|
x > y
|
3/2
|
5
|
x < y
|
5/3
|
1/2
|
x > y
|
5/3
|
5
|
x < y
|
∴ After comparing x and y both, No relation in x and y or x = y.