Equations And Inequations Ques 86
I. $3 x^{2}-10 x+3=0$
II. $y^{2}-5 y+6=0$
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: 86.(4)
Solution: (4) I. $3 x^{2}-10 x+3=0$
$\Rightarrow 3 x^{2}-9 x-x+3=0$
$\Rightarrow 3 x(x-3)-1(x-3)=0$
$\Rightarrow(x-3)(3 x-1)=0$
$\Rightarrow x=3$ or, $\frac{1}{3}$ II. $y^{2}-5 y+6=0$
$\Rightarrow y^{2}-2 y-3 y+6=0$
$\Rightarrow y(y-2)-3(y-2)=0$
$\Rightarrow(y-2)(y-3)=0$
$\Rightarrow y=2$ or, 3
Clearly, $x \leq y$
BETA
