Correct Answer - Option 5 : x = y or relation between x and y can not be established.
Given:
I. 3x2 - 4x - 32 = 0
II. 9y2 - 29y + 22 = 0
Calculation:
From I,
3x2 - 4x - 32 = 0
⇒ 3x2 - 12x + 8x - 32 = 0
⇒ 3x(x - 4) + 8(x - 4) = 0
⇒ (x - 4)(3x + 8) = 0
Taking,
⇒ (x - 4) = 0 or (3x + 8) = 0
⇒ x = 4 or (-8/3)
From II,
9y2 - 29y + 22 = 0
⇒ 9y2 - 18y - 11y + 22 = 0
⇒ 9y(y - 2) - 11(y - 2) = 0
⇒ (y - 2)(9y - 11) = 0
Taking,
⇒ (y - 2) = 0 or (9y - 11) = 0
⇒ y = 2 or (11/9)
Comparison between x and y (via Tabulation):
Value of x
|
Value of y
|
Relation
|
4
|
2
|
x > y
|
4
|
11/9
|
x > y
|
-8/3
|
2
|
x < y
|
-8/3
|
11/9
|
x < y
|
∴ x = y or relation between x and y can not be established.