Correct Answer - Option 4 : x ≤ y
I. \(3{x^2} - 22x + 7 = 0\)
\( \Rightarrow 3{x^2} - x - 21x + 7 = 0\)
\( \Rightarrow x\left( {3x - 1} \right) - 7\left( {3x - 1} \right) = 0\)
\( \Rightarrow \left( {x - 7} \right)\left( {3x - 1} \right) = 0\)
\( \Rightarrow x = 7\,or\,\frac{1}{3}\)
II. \({y^2} - 15y + 56 = 0\)
\( \Rightarrow {y^2} - 8y - 7y + 56 = 0\)
\( \Rightarrow y\left( {y - 8} \right) - 7\left( {y - 8} \right) = 0\)
\( \Rightarrow \left( {y - 7} \right)\left( {y - 8} \right) = 0\)
\( \Rightarrow y = 7\,or\,\,8\)
Comparison between x and y (via Tabulation):
|
Value of x
|
Value of y
|
Relation
|
|
7
|
7
|
x = y
|
|
7
|
8
|
x < y
|
|
1/3
|
7
|
x < y
|
|
1/3
|
8
|
x < y
|
∴ x ≤ y
