Equations And Inequations Ques 106
I. $2 x^{2}-21 x+54=0$
II. $y^{2}-14 y+49=0$
Directions : In the following questions two equations numbered 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 the relationship between $x$ and $y$ cannot be established.
Show Answer
Correct Answer: 106.(3)
Solution: (3) I. $2 x^{2}-21 x+54=0$
$\Rightarrow 2 x^{2}-12 x-9 x+54=0$
$\Rightarrow 2 x(x-6)-9(x-6)=0$
$\Rightarrow(x-6)(2 x-9)=0$
$\Rightarrow x=6$ or, $\frac{9}{2}$
II. $y^{2}-14 y+49=0$
$\Rightarrow(y-7)^{2}=0 \Rightarrow y-7=0$
$\Rightarrow y=7$
Clearly, $x<y$
BETA
