Equations And Inequations Ques 107
I. $x^{2}-19 x+70=0$
II. $2 y^{2}-17 y+35=0$
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: 107.(2)
Solution: (2) I. $x^{2}-19 x+70=0$
$\Rightarrow x^{2}-5 x-14 x+70=0$
$\Rightarrow x(x-5)-14(x-5)=0$
$\Rightarrow(x-5)(x-14)=0$
$\Rightarrow x=5$ or, 14
II. $2 y^{2}-17 y+35=0$
$\Rightarrow 2 y^{2}-10 y-7 y+35=0$
$\Rightarrow 2 y(y-5)-7(y-5)=0$
$\Rightarrow(y-5)(2 y-7)=0$
$\Rightarrow y=5$ or, $\frac{7}{2}$
Clearly, $x \geq y$
BETA
