Equations And Inequations Ques 66
I. $4 x^{2}-12 x+5=0$
II. $4 y^{2}-8 y+3=0$
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: 66.(2)
Solution: (2) I. $4 x^{2}-12 x+5=0$ $\Rightarrow 4 x^{2}-2 x-10 x+5=0$ $\Rightarrow 2 x(2 x-1)-5(2 x-1)=0$ $\Rightarrow(2 x-1)(2 x-5)=0$
$\Rightarrow x=\frac{1}{2}$ or, $\frac{5}{2}$
II. $4 y^{2}-8 y+3=0$
$\Rightarrow 4 y^{2}-2 y-6 y+3=0$
$\Rightarrow 2 y(2 y-1)-3(2 y-1)=0$
$\Rightarrow(2 y-1)(2 y-3)=0$
$\Rightarrow y=\frac{1}{2}$ or, $\frac{3}{2}$
Clearly, $x \geq y$
BETA
