Equations And Inequations Ques 144
I. $x^{2}+5 x+6=0$
II. $y^{2}+7 y+12=0$
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: (1)
Solution: (1) I. $x^{2}+5 x+6=0$
$\Rightarrow x^{2}+2 x+3 x+6=0$
$\Rightarrow x(x+2)+3(x+2)=0$
$\Rightarrow(x+3)(x+2)=0$
$\Rightarrow x=-3$ or -2
II. $y^{2}+7 y+12=0$
$\Rightarrow y^{2}+4 y+3 y+12=0$
$\Rightarrow y(y+4)+3(y+4)=0$
$\Rightarrow(y+3)(y+4)=0$
$\Rightarrow y=-3$ or -4
Clearly, $x \geq y$
BETA
