Equations And Inequations Ques 145
I. $x^{2}+20=9 x$
II. $y^{2}+42=13 y$
Directions : In each of the following questions two equations are given. Solve these equations and give answer :
(1) if $x \geq y$, i.e., $x$ is greater than or equal to $y$
(2) if $x>y$, i.e., $x$ is greater than $y$
(3) if $x \leq y$, i.e., $x$ is less than or equal to $y$
(4) if $x<y$, i.e., $x$ less than $y$
(5) $x=y$ or no relation can be established between $x$ and $y$
(IBPS Specialist Officer CWE 17.03.2013)
Show Answer
Correct Answer: (4)
Solution: (4) I. $x^{2}-9 x+20=0$
$\Rightarrow x^{2}-5 x-4 x+20=0$
$\Rightarrow x(x-5)-4(x-5)=0$
$\Rightarrow(x-4)(x-5)=0$
$\Rightarrow x=4$ or 5
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, $x<y$
BETA
