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.