Equations And Inequations Ques 83
I. $12 x^{2}+11 x+12=10 x^{2}+22 x$
II. $13 y^{2}-18 y+3=9 y^{2}-10 y$
Directions : In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer If
(1) $x>y$
(2) $\quad x \geq y$
(3) $x<y$
(4) $x \leq y$
(5) $x=y$ or the relationship cannot be established
(Bank Of Baroda PO Exam.13.03.2011)
Show Answer
Correct Answer: (2)
Solution: (2) I. $12 x^{2}+11 x+12-10 x^{2}$ $-22 x=0$
$\Rightarrow 2 x^{2}-11 x+12=0$
$\Rightarrow 2 x^{2}-8 x-3 x+12=0$
$\Rightarrow 2 x(x-4)-3(x-4)=0$
$\Rightarrow(x-4)(2 x-3)=0$
$\Rightarrow x=4$ or $\frac{3}{2}$
II. $13 y^{2}-18 y+3-9 y^{2}+10 y$
$=0$
$\Rightarrow 4 y^{2}-8 y+3=0$
$\Rightarrow 4 y^{2}-6 y-2 y+3=0$
$\Rightarrow 2 y(2 y-3)-1(2 y-3)=0$
$\Rightarrow(2 y-1)(2 y-3)=0$
$\Rightarrow y=\frac{1}{2}$ or $\frac{3}{2}$
Clearly, $x>y$
BETA
