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. $16{{x}^{2}}+32x+5=0$
II. $12{{y}^{2}}-17y+6=0$
$x \lt y$
$x \gt y$
$x \le y$
$x \ge y$
$x = y$ or relationship between $x$ & $y$ can not be established
Solution
I.
$\begin{align}
& 16{{x}^{2}}+32x+15=0 \\
& \Rightarrow 16{{x}^{2}}+20x+12x+15=0 \\
& \Rightarrow 4x(4x+5)+3(4x+5)=0 \\
& \Rightarrow (4x+3)(4x+5)=0 \\
& \Rightarrow x=-\frac{3}{4}or-\frac{5}{4} \\
\end{align}$
II.
$\begin{align}
& 12{{y}^{2}}+17y+6=0 \\
& \Rightarrow 12{{y}^{2}}+9y+8y+6=0 \\
& \Rightarrow 3y(4y+3)+2(4y+3)=0 \\
& \Rightarrow (3y+2)(4y+3)=0 \\
& \Rightarrow y=-\frac{2}{3}or-\frac{3}{4} \\
\end{align}$
So, $x\le y$