Equations And Inequations Ques 85
I. $2 x^{2}-11 x+15=0$
II. $2 y^{2}-15 y+28=0$
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 $x \leq y$
(5) if $x=y$ or the relationship between $x$ and $y$ cannot be established.
Show Answer
Correct Answer: 85.(3)
Solution: (3) I. $2 x^{2}-11 x+15=0$
$\Rightarrow 2 x^{2}-6 x-5 x+15=0$
$\Rightarrow 2 x(x-3)-5(x-3)=0$
$\Rightarrow(x-3)(2 x-5)=0$
$\Rightarrow x=3$ or, $\frac{5}{2}$
II. $2 y^{2}-15 y+28=0$
$\Rightarrow 2 y^{2}-8 y-7 y+28=0$
$\Rightarrow 2 y(y-4)-7(y-4)=0$
$\Rightarrow(y-4)(2 y-7)=0$
$\Rightarrow y=4$ or, $\frac{7}{2}$
Clearly, $x<y$
BETA
