Equations And Inequations Ques 67
I. $10 x^{2}+21 x+8=0$
II. $5 y^{2}+19 y+18=0$
Directions : In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer
(1) if $x>y$
(2) if $x \geq y$
(3) if $x<y$
(4) if $x \leq y$
(5) if $x=y$ or relationship between $x$ and $y$ cannot be established.
Show Answer
Correct Answer: 67.(1)
Solution: (1) I. $10 x^{2}+21 x+8=0$
$\Rightarrow 10 x^{2}+5 x+16 x+8=0$
$\Rightarrow 5 x(2 x+1)+8(2 x+1)=0$
$\Rightarrow(2 x+1)(5 x+8)=0$
$\Rightarrow x=-\frac{1}{2}$ or, $-\frac{8}{5}$
II. $5 y^{2}+19 y+18=0$
$\Rightarrow 5 y^{2}+10 y+9 y+18=0$
$\Rightarrow 5 y(y+2)+9(y+2)=0$
$\Rightarrow(y+2)(5 y+9)=0$
$\Rightarrow y=-2$ or, $-\frac{9}{5}$
Clearly, $x>y$
BETA
