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. $9{{x}^{2}}-4=0$
II. $3{{y}^{2}}-23y+14=0$
$x \lt y$
$x \gt y$
$x \le y$
$x \ge y$
$x = y$ or relationship between $x$ & $y$ can not be established
Solution
I.
$\begin{align}
& 9{{x}^{2}}-4=0 \\
& \Rightarrow (3x-2)(3x+2)=0 \\
& \Rightarrow x=\frac{2}{3}or-\frac{2}{3} \\
\end{align}$
II.
$\begin{align}
& 3{{y}^{2}}-23y+14=0 \\
& \Rightarrow 3{{y}^{2}}-2y-21y+14=0 \\
& \Rightarrow y(3y-2)-7(3y-2)=0 \\
& \Rightarrow (y-7)(3y-2)=0 \\
& \Rightarrow y=7or\frac{2}{3} \\
\end{align}$
So, $x\le y$