Equations And Inequations Ques 173
I. $3 x^{2}-21 x+18=0$
II. $y^{2}-13 y+42=0$
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) $x \geq y$
(3) $x<y$
(4) $x \leq y$
(5) $\quad x=y$ or the relationship cannot be established
(SIDBI Bank Officer Exam. 09.09.2014)
Show Answer
Correct Answer: (4)
Solution: (4) I. $3 x^{2}-21 x+18=0$
$\Rightarrow x^{2}-7 x+6=0$
$\Rightarrow x^{2}-6 x-x+6=0$
$\Rightarrow x(x-6)-1(x-6)=0$
$\Rightarrow(x-1)(x-6)=0$
$\Rightarrow x=1$ or 6
II. $y^{2}-13 y+42=0$
$\Rightarrow y^{2}-7 y-6 y+42=0$
$\Rightarrow y(y-7)-6(y-7)=0$
$\Rightarrow(y-6)(y-7)=0$
$\Rightarrow y=6$ or 7
Clearly, $x \leq y$
BETA
