Equations And Inequations Ques 124
I. $2 x^{2}+23 x+63=0$
II. $4 y^{2}+19 y+21=0$
Directions : In each of the following questions, two equations I and II are given. You have to solve both the equations and give answer
(1) if $x<y$
(2) if $x>y$
(3) if $x \leq y$
(4) if $x \geq y$
(5) if $x=y$ or the relationship between $x$ and $y$ can not be established.
Show Answer
Correct Answer: 124.(1)
Solution: (1) I. $2 x^{2}+23 x+63=0$
$\Rightarrow 2 x^{2}+14 x+9 x+63=0$
$\Rightarrow 2 x(x+7)+9(x+7)=0$
$\Rightarrow(x+7)(2 x+9)=0$
$\Rightarrow x=-7$ or $-\frac{9}{2}$
II. $4 y^{2}+19 y+21=0$
$\Rightarrow 4 y^{2}+12 y+7 y+21=0$
$\Rightarrow 4 y(y+3)+7(y+3)=0$
$\Rightarrow(y+3)(4 y+7)=0$
$\Rightarrow y=-3$ or $-\frac{7}{4}$
Clearly, $x<y$
BETA
