Equations And Inequations Ques 62
I. $3 x^{2}-10 x+8=0$
II. $2 y^{2}-19 y+35=0$
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: 62.(3)
Solution: (3) I. $3 x^{2}-10 x+8=0$
$\Rightarrow 3 x^{2}-6 x-4 x+8=0$
$\Rightarrow 3 x(x-2)-4(x-2)=0$
$\Rightarrow(3 x-4)(x-2)=0$
$\Rightarrow x=\frac{4}{3}$ or, 2
II. $2 y^{2}-19 y+35=0$
$\Rightarrow 2 y^{2}-14 y-5 y+35=0$
$\Rightarrow 2 y(y-7)-5(y-7)=0$
$\Rightarrow(y-7)(2 y-5)=0$
$\Rightarrow y=7$ or, $\frac{5}{2}$
Clearly, $x<y$
BETA
