Equations And Inequations Ques 3
I. $2 x^{2}-9 x+10=0$
II. $2 y^{2}-13 y+20=0$
(1) $ x \leq y $
(2) $ x \geq y$
(3) relationship between $x$ and $y$ cannot be determined
(4) $x<y$
(5) $x>y$
Show Answer
Correct Answer: 3.(1)
Solution: (1) I. $2 x^{2}-9 x+10=0$
$\Rightarrow 2 x^{2}-4 x-5 x+10=0$
$\Rightarrow 2 x(x-2)-5(x-2)=0$
$\Rightarrow(x-2)(2 x-5)=0$
$\Rightarrow x=2$ or $x=\frac{5}{2}$
II. $2 y^{2}-13 y+20=0$
$\Rightarrow 2 y^{2}-8 y-5 y+20=0$
$\Rightarrow 2 y(y-4)-5(y-4)=0$
$\Rightarrow(y-4)(2 y-5)=0$
$\Rightarrow y=4$ or $\frac{5}{2}$
Clearly, $x \leq y$
BETA
