Equations And Inequations Ques 125
I. $3 x^{2}+29 x+56=0$
II. $2 y^{2}+15 y+25=0$
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: 125.(1)
Solution: (1) I. $3 x^{2}+29 x+56=0$
$\Rightarrow 3 x^{2}+21 x+8 x+56=0$
$\Rightarrow 3 x(x+7)+8(x+7)=0$
$\Rightarrow(x+7)(3 x+8)=0$
$\Rightarrow x=-7$ or $\frac{-8}{3}$
II. $2 y^{2}+15 y+25=0$
$\Rightarrow 2 y^{2}+10 y+5 y+25=0$
$\Rightarrow 2 y(y+5)+5(y+5)=0$
$\Rightarrow(y+5)(2 y+5)=0$
$\Rightarrow y=-5$ or $-\frac{5}{2}$
Clearly, $x<y$
BETA
