Equations And Inequations Ques 65
I. $6 x^{2}-19 x+15=0$
II. $5 y^{2}-22 y+24=0$
Directions : In each of these questions, two equations (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 relationship between $x$ and $y$ cannot be established.
Show Answer
Correct Answer: 65.(3)
Solution: (3) I. $6 x^{2}-19 x+15=0$ $\Rightarrow 6 x^{2}-9 x-10 x+15=0$ $\Rightarrow 3 x(2 x-3)-5(2 x-3)=0$ $\Rightarrow(2 x-3)(3 x-5)=0$
$\Rightarrow x=\frac{3}{2}$ or, $\frac{5}{3}$
II. $5 y^{2}-22 y+24=0$
$\Rightarrow 5 y^{2}-10 y-12 y+24=0$
$\Rightarrow 5 y(y-2)-12(y-2)=0$
$\Rightarrow(y-2)(5 y-12)=0$
$\Rightarrow y=2$ or, $\frac{12}{5}$
Clearly, $x<y$
BETA
