Equations And Inequations Ques 21
I. $2 x^{2}-13 x+18=0$
II. $2 y^{2}-19 y+45=0$
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) $x>y$
(3) $x \leq y$
(4) $x \geq y$
(5) $\quad x=y$ or the relationship cannot be established
(SIDBI Officer Online Exam.24.02.2016)
Show Answer
Correct Answer: 21.(3)
Solution: (3) I. $2 x^{2}-13 x+18=0$
$\Rightarrow 2 x^{2}-4 x-9 x+18=0$
$\Rightarrow 2 x(x-2)-9(x-2)=0$
$\Rightarrow(x-2)(2 x-9)=0$
$\Rightarrow x=2$ or, $\frac{9}{2}$ II. $2 y^{2}-19 y+45=0$
$\Rightarrow 2 y^{2}-10 y-9 y+45=0$
$\Rightarrow 2 y(y-5)-9(y-5)=0$
$\Rightarrow(2 y-9)(y-5)=0$
$\Rightarrow y=\frac{9}{2}$ or, 5
Clearly, $x \leq y$
BETA
