Equations And Inequations Ques 58
I. $2 x^{2}-13 x+21=0$
II. $3 y^{2}-14 y+15=0$
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: 58.(2)
Solution: (2) I. $2 x^{2}-13 x+21=0$
$\Rightarrow 2 x^{2}-6 x-7 x+21=0$
$\Rightarrow 2 x(x-3)-7(x-3)=0$
$\Rightarrow(x-3)(2 x-7)=0$ $\Rightarrow x=3$ or, $\frac{7}{2}$
II. $3 y^{2}-14 y+15=0$
$\Rightarrow 3 y^{2}-9 y-5 y+15=0$
$\Rightarrow 3 y(y-3)-5(y-3)=0$
$\Rightarrow(y-3)(3 y-5)=0$
$\Rightarrow y=3$ or, $\frac{5}{3}$
Clearly, $x \geq y$
BETA
