Correct Answer - Option 5 :
x = y or relationship between x and y cannot be established
I.\({x^2} - 14x + 48 = 0\)
\( ⇒ {x^2} - 6x - 8x + 48 = 0\)
\( ⇒ x\left( {x - 6} \right) - 8\left( {x - 6} \right) = 0\)
\( ⇒ \left( {x - 6} \right)\left( {x - 8} \right) = 0\)
⇒ x = 6 or 8
II. \({y^2} - 16y + 63 = 0\)
\( ⇒ {y^2} - 9y - 7y + 63 = 0\)
\( ⇒ y\left( {y - 9} \right) - 7\left( {y - 9} \right) = 0\)
\( ⇒ \left( {y - 7} \right)\left( {y - 9} \right) = 0\)
⇒ y = 7 or 9
Comparison between x and y (via Tabulation):
Value of x
|
Value of y
|
Relation
|
6
|
7
|
x < y
|
6
|
9
|
x < y
|
8
|
7
|
x > y
|
8
|
9
|
x < y
|
∴ x = y or relationship between x and y cannot be established