Equations And Inequations Ques 49
I. $3 x^{2}-19 x+28=0$
II. $5 y^{2}-18 y+16=0$
Directions : In the following questions two equations numbered 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 $x<y$
(5) if $x=y$ or the relationship cannot be established
(UCO Bank PO Exam. 30.01.2011)
Show Answer
Correct Answer: (1)
Solution: (1) I. $3 x^{2}-19 x+28=0$
$\Rightarrow 3 x^{2}-12 x-7 x+28=0$
$\Rightarrow 3 x(x-4)-7(x-4)=0$
$\Rightarrow(x-4)(3 x-7)=0$
$\therefore x=4$ or $\frac{7}{3}$
II. $5 y^{2}-18 y+16=0$
$\Rightarrow 5 y^{2}-10 y-8 y+16=0$
$\Rightarrow 5 y(y-2)-8(y-2)=0$
$\Rightarrow(5 y-8)(y-2)=0$
$\therefore y=\frac{8}{5}$ or 2
Clearly, $x>y$
BETA
