Equations And Inequations Ques 68
I. $6 x^{2}-5 x+1=0$
II. $12 y^{2}-23 y+10=0$
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: 68.(3)
Solution: (3) I. $6 x^{2}-5 x+1=0$
$\Rightarrow 6 x^{2}-3 x-2 x+1=0$
$\Rightarrow 3 x(2 x-1)-1(2 x-1)=0$
$\Rightarrow(2 x-1)(3 x-1)=0$
$\Rightarrow x=\frac{1}{2}$ or, $\frac{1}{3}$
II. $12 y^{2}-23 y+10=0$
$\Rightarrow 12 y^{2}-8 y-15 y+10=0$
$\Rightarrow 4 y(3 y-2)-5(3 y-2)=0$
$\Rightarrow(3 y-2)(4 y-5)=0$
$\Rightarrow y=\frac{2}{3}$ or, $\frac{5}{4}$
Clearly, $x<y$
BETA
