Directions for Questions 31 - 35: In each question two equations numbered I and II are given. You have to solve both the equations and mark answer:
I. $81{{x}^{2}}-63x+12=0$
II. $20{{y}^{2}}-9y+1=0$
$x \lt y$
$x \gt y$
$x\le y$
$x\ge y$
$x=y$ or relationship between $x$ and $y$ cannot be established
Solution
I. $81{{x}^{2}}-63x+12=0$
$81{{x}^{2}}-~\left( 36+27 \right)x+12=0$
$81{{x}^{2}}-~36x-27x+12=0$
$9x\left( 9x-4 \right)-3\left( 9x-4 \right)=0$
$\left( 9x-4 \right)\left( 9x-3 \right)=0$
$x=~\dfrac{4}{9},~\dfrac{1}{3}$
II. $20{{y}^{2}}-9y+1=0$
$20{{y}^{2}}-\left( 5+4 \right)y+1=0$
$20{{y}^{2}}-5y-4y+1=0$
$5y\left( 4y-1 \right)-1\left( 4y-1 \right)=0$
$\left( 4y-1 \right)\left( 5y-1 \right)=0$
$y=\dfrac{1}{4},~\dfrac{1}{5}$
After comparison both equations, the conclusion is
$x \gt y$