Equations And Inequations Ques 111
I. $x^{2}-19 x+84=0$
II. $y^{2}-25 y+156=0$
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
(Indian Overseas Bank PO Exam. 22.05.2011)
Show Answer
Correct Answer: (4)
Solution: (4) I. $x^{2}-19 x+84=0$
$\Rightarrow x^{2}-12 x-7 x+84=0$
$\Rightarrow x(x-12)-7(x-12)=0$
$\Rightarrow(x-7)(x-12)=0$
$\therefore x=7$ or 12
II. $y^{2}-25 y+156=0$
$\Rightarrow y^{2}-12 y-13 y+156=0$
$\Rightarrow y(y-12)-13(y-12)=0$
$\Rightarrow(y-13)(y-12)=0$
$\therefore y=13$ or 12
Clearly, $x \leq y$
BETA
