Correct Answer - Option 5 :
x = y or relation between x and y can not be established.
Given:
I. 3x2 – 4x - 32 = 0
II. 7y2 – 8y - 12 = 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,
II. 7y2 – 8y - 12 = 0
⇒ 7y2 – 14y + 6y - 12 = 0
⇒ 7y(y - 2) + 6(y - 2) = 0
⇒ (y - 2)(7y + 6) = 0
Taking,
⇒ (y - 2) = 0 or (7y + 6) = 0
⇒ y = 2 or (-6/7)
Comparison between x and y (via Tabulation):
Value of x
|
Value of y
|
Relation
|
4
|
2
|
x > y
|
4
|
-6/7
|
x > y
|
-8/3
|
2
|
x < y
|
-8/3
|
-6/7
|
x < y
|
∴ x = y or relation between x and y can not be established.