Directions (51 - 55): In these questions two equations numbered I and II are given. You have to solve both the equations and give answer.
Give Answer (A) if $x \lt y$
Give Answer (B) if $x \gt y$
Give Answer (C) if $x \le y$
Give Answer (D) if $x \ge y$
Give Answer (E) if $x = y$ or relationship between $x$ & $y$ can not be established
I. $14{{x}^{2}}-11x+2=0$
II. $14{{y}^{2}}+9y+1=0$
$x \lt y$
$x \gt y$
$x \le y$
$x \ge y$
$x = y$ or relationship between $x$ & $y$ can not be established
Solution
I.
$\begin{align}
& 14{{x}^{2}}-11x+2=0 \\
& \Rightarrow 14{{x}^{2}}-7x-4x+2=0 \\
& \Rightarrow 7x(2x-1)-2(2x-1)=0 \\
& \Rightarrow (7x-2)(2x-1)=0 \\
& \Rightarrow x=\frac{2}{7}or\frac{1}{2} \\
\end{align}$
II.
$\begin{align}
& 14{{y}^{2}}+9y+1=0 \\
& \Rightarrow 14{{y}^{2}}+7y+2y+1=0 \\
& \Rightarrow 7y(2y+1)+1(2y+1)=0 \\
& \Rightarrow (7y+1)(2y+1)=0 \\
& \Rightarrow y=-\frac{1}{7}or-\frac{1}{2} \\
\end{align}$
So, $x \gt y$