Correct Answer - Option 3 : x = y or the relationship cannot be established.
I. 8x2 – 32x + 14 = 0
⇒ 8x2 – 28x – 4x + 14 = 0
⇒ 4x(2x – 7) – 2(2x – 7) = 0
⇒ (2x – 7)(4x – 2) = 0
⇒ x = 7/2 or 1/2
II. 3y2 – 37y – 26 = 0
⇒ 3y2 – 39y + 2y – 26 = 0
⇒ 3y(y – 13) + 2(y – 13) = 0
⇒ (y – 13)(3y + 2) = 0
⇒ y = 13 or -(2/3)
Comparison between x and y (via Tabulation):
Value of x
|
Relation
|
Value of y
|
7/2
|
<
|
13
|
7/2
|
>
|
-(2/3)
|
1/2
|
<
|
13
|
1/2
|
>
|
-(2/3)
|
∴ Relationship cannot be established between x and y.