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.