Equations And Inequations Ques 91
I. $6 x^{2}-5 x+1=0$
II. $4 y^{2}-8 y+3=0$
Directions : In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answe If
(1) $x<y$
(2) $x>y$
(3) $x \leq y$
(4) $x \geq y$
(5) $x=y$ or the relationship cannot be established
Show Answer
Correct Answer: 91.(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. $4 y^{2}-8 y+3=0$
$\Rightarrow 4 y^{2}-2 y-6 y+3=0$
$\Rightarrow 2 y(2 y-1)-3(2 y-1)=0$
$\Rightarrow(2 y-3)(2 y-1)=0$
$\Rightarrow y=\frac{3}{2}$ or, $\frac{1}{2}$
Clearly, $x \leq y$
BETA
