Correct Answer  Option 5 :
x = y or relation between x and y can not be established.
Given:
I. 6x2  23x + 20 = 0
II. y2  5y + 4 = 0
Calculation:
From I,
6x2  23x + 20 = 0
⇒ 6x2  15x  8x + 20 = 0
⇒ 3x(2x  5)  4(2x  5) = 0
⇒ (2x  5)(3x  4) = 0
Taking,
⇒ (2x  5) = 0 or (3x  4) = 0
⇒ x = (5/2) or (4/3)
From II,
y2  5y + 4 = 0
⇒ y2  4y  y + 4 = 0
⇒ y(y  4)  1(y  4) = 0
⇒ (y  4)(y  1) = 0
Taking,
⇒ (y  4) = 0 or (y  1) = 0
⇒ y = 4 or 1
Comparison between x and y (via Tabulation):
Value of x

Value of y

Relation

5/2

4

x < y

5/2

1

x > y

4/3

4

x < y

4/3

1

x > y

∴ x = y or relation between x and y can not be established.