Equations And Inequations Ques 96
I. $5 x^{2}-13 x+6=0$
II. $2 y^{2}-7 y+6=0$
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: 96.(3)
Solution: (3) I. $5 x^{2}-13 x+6=0$
$\Rightarrow 5 x^{2}-10 x-3 x+6=0$
$\Rightarrow 5 x(x-2)-3(x-2)=0$ $\Rightarrow(x-2)(5 x-3)=0$
$\Rightarrow x=2$ or, $\frac{3}{5}$
II. $2 y^{2}-7 y+6=0$
$\Rightarrow 2 y^{2}-4 y-3 y+6=0$
$\Rightarrow 2 y(y-2)-3(y-2)=0$
$\Rightarrow(y-2)(2 y-3)=0$
$\Rightarrow y=2$ or, $\frac{3}{2}$
Clearly, $x \leq y$
BETA
