Equations And Inequations Ques 163
I. $38 x^{2}-3 x-11=0$
II. $28 y^{2}+32 y+9=0$
Directions : In the following questions, two equations I and II have been given. You have to solve both equations and give answer if
(1) $x>y$
(2) $x \geq y$
(3) $x<y$
(4) $x \leq y$
(5) $x=y$ or the relation cannot be established.
(Bank of Baroda PO Exam. 14.08.2014)
Show Answer
Correct Answer: (2)
Solution: (2) I. $38 x^{2}-3 x-11=0$
$\Rightarrow 38 x^{2}-22 x+19 x-11=0$
$\Rightarrow 2 x(19 x-11)+1(19 x-11)$
$=0$
$\Rightarrow(2 x+1)(19 x-11)=0$
$\Rightarrow x=-\frac{1}{2}$ or $\frac{11}{19}$
II. $28 y^{2}+32 y+9$
$\Rightarrow 28 y^{2}+14 y+18 y+9=0$
$\Rightarrow 14 y(2 y+1)+9(2 y+1)=0$
$\Rightarrow(14 y+9)(2 y+1)=0$
$\Rightarrow y=-\frac{9}{14}$ or $-\frac{1}{2}$
Clearly, $x \geq y$
BETA
