Equations And Inequations Ques 77
I. $x^{2}-7 x+12=0$
II. $3 y^{2}-11 y+10=0$
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: 77.(1)
Solution: (1) I. $x^{2}-7 x+12=0$
$\Rightarrow x^{2}-4 x-3 x+12=0$
$\Rightarrow x(x-4)-3(x-4)=0$
$\Rightarrow(x-3)(x-4)=0$
$\Rightarrow x=3$ or, 4
II. $3 y^{2}-11 y+10=0$
$\Rightarrow 3 y^{2}-6 y-5 y+10=0$
$\Rightarrow 3 y(y-2)-5(y-2)=0$
$\Rightarrow(y-2)(3 y-5)=0$
$\Rightarrow y=2$ or, $\frac{5}{3}$
Clearly, $x>y$
BETA
