Equations And Inequations Ques 117
I. $x^{2}-5 x+6=0$
II. $5 y^{2}-18 y+16=0$
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: 117.(2)
Solution: (2) I. $x^{2}-5 x+6=0$
$\Rightarrow x^{2}-2 x-3 x+6=0$
$\Rightarrow x(x-2)-3(x-2)=0$
$\Rightarrow(x-2)(x-3)=0$
$\Rightarrow x=2$ or, 3
II. $5 y^{2}-18 y+16=0$
$\Rightarrow 5 y^{2}-10 y-8 y+16=0$
$\Rightarrow 5 y(y-2)-8(y-2)=0$
$\Rightarrow y=2$ or, $\frac{8}{5}$
Clearly, $x \geq y$
BETA
