Equations And Inequations Ques 164
I. $9 x^{2}-27 x+8=0$
II. $4 y^{2}-13 y+3=0$
Directions : In each of the following questions two equations I and II have been 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 cannot be established between them
(IDBI Officer Grade Exam. 22.08.2014)
Show Answer
Correct Answer: (5)
Solution: (5) I. $9 x^{2}-27 x+8=0$
$\Rightarrow 9 x^{2}-24 x-3 x+8=0$
$\Rightarrow 3 x(3 x-8)-1(3 x-8)=0$
$\Rightarrow(3 x-1)(3 x-8)=0$
$\therefore x=\frac{1}{3}$ or $\frac{8}{3}$
II. $4 y^{2}-13 y+3=0$
$\Rightarrow 4 y^{2}-12 y-y+3=0$
$\Rightarrow 4 y(y-3)-1(y-3)=0$
$\Rightarrow(4 y-1)(y-3)=0$
$\therefore y=\frac{1}{4}$ or 3
BETA
