Correct Answer - Option 3 : x ≥ y
Calculations:
From I,
2x2 - (4 + √13)x + 2√13 = 0
⇒ 2x2 - 4x - √13x + 2√13 = 0
⇒ 2x(x - 2) - √13(x - 2) = 0
⇒ (2x - √13)(x - 2) = 0
Taking,
⇒ 2x - √13 = 0 or x - 2 = 0
⇒ x = √13/2 or x = 2
From II,
10y2 - (18 + 5√13)y + 9√13 = 0
⇒ 10y2 - 18y - 5√13y + 9√13 = 0
⇒ 2y(5y - 9) - √13(5y - 9) = 0
⇒ (5y - 9)(2y - √13) = 0
Taking,
⇒ 5y - 9 = 0 or 2y - √13 = 0
⇒ y = 9/5 or y = √13/2
Comparison between x and y (via Tabulation):
x
|
Y
|
Relation
|
√13/2
|
9/5
|
x = y
|
√13/2
|
√13/2
|
x = y
|
2
|
9/5
|
x > y
|
2
|
√13/2
|
x > y
|
∴ After comparing x and y both, x ≥ y.