Correct Answer - Option 2 : x < y
I. \(6{x^2} - 7x + 2 = 0\)
\( \Rightarrow 6{x^2} - 3x - 4x + 2 = 0\)
\( \Rightarrow 3x\left( {2x - 1} \right) - 2\left( {2x - 1} \right) = 0\)
\( \Rightarrow \left( {2x - 1} \right)\left( {3x - 2} \right) = 0\)
\( \Rightarrow x = \frac{1}{2}\) or \(\frac{2}{3}\)
II. \(2{y^2} - 5y + 3 = 0\)
\( \Rightarrow 2{y^2} - 2y - 3y + 3 = 0\)
\( \Rightarrow 2y\left( {y - 1} \right) - 3\left( {y - 1} \right) = 0\)
\( \Rightarrow \left( {y - 1} \right)\left( {2y - 3} \right) = 0\)
\( \Rightarrow y = 1\) or \(\frac{3}{2}\)
Comparison between x and y (via Tabulation):
Value of x
|
Value of y
|
Relation
|
1/2
|
1
|
x < y
|
1/2
|
3/2
|
x < y
|
2/3
|
1
|
x < y
|
2/3
|
3/2
|
x < y
|
∴ Clearly x < y