Equations And Inequations Ques 41
I. $4 x^{2}-15 x+14=0$
II. $6 y^{2}-10 y+4=0$
Directions : In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer If
(1) $x<y$
(2) $x>y$
(3) $x \leq y$
(4) $x \geq y$
(5) $\quad x=y$ or the relationship cannot be established
(IBPS Bank PO/MT (Pre.) Exam, 23.10.2016)
Show Answer
Correct Answer: 41.(2)
Solution: (2) I. $4 x^{2}-15 x+14=0$
$\Rightarrow 4 x^{2}-8 x-7 x+14=0$
$\Rightarrow 4 x(x-2)-7(x-2)=0$
$\Rightarrow(x-2)(4 x-7)=0$
$\Rightarrow x=2$ or, $\frac{7}{4}$
II. $6 y^{2}-10 y+4=0$
$\Rightarrow 3 y^{2}-5 y+2=0$
$\Rightarrow 3 y^{2}-3 y-2 y+2=0$
$\Rightarrow 3 y(y-1)-2(y-1)=0$
$\Rightarrow(y-1)(3 y-2)=0$
$\Rightarrow y=1$ or, $\frac{2}{3}$
Clearly, $x>y$
BETA
