Hi jaheer,

For all inequalities, be sure to know the sign of each number before to simplify any inequality;
What you did to reach the following expresion (r^2+2)>pr from 1/P > r/(r^2+2) is that you have multiplied by P and then by ( r^2+2) EACH side of the inequality,
you can not do that untless you know the sign of P,
Therfore, 1 and 2 together give suffisants conditions to answer the question,

If you are still not confident with, consider 1 that tell p=r without any information about the sign; than we can pick 1 and -1 as values of p and r;
in the first case p=r=1 ; 1/r =1 > 1/( 2+2) ( it's fine)
in the second case,p=r=-1; 1/r = -1 and ( r/( r^2+2) )= -1/3 ( it's not much fine here)

I hope I am right and clear[/b]

Aha! Thanks. Got it.

Your "Frenchy English" is not bad at all ( except for few French Spellings ).

Good Luck.

wonderful explanation. I am a bit conufesed on one think.. I made the same mistake of simplifying without paying respect to the rules..

What is the takeaway here. WHen can we simplify?

The reason i ask is there is no negative sign in from of p or and r^2 is obviously positive. THerefore arent all pos and neg signs accounted for?

wonderful explanation. I am a bit conufesed on one think.. I made the same mistake of simplifying without paying respect to the rules..

What is the takeaway here. WHen can we simplify?

The reason i ask is there is no negative sign in from of p or and r^2 is obviously positive. THerefore arent all pos and neg signs accounted for?

note that on this solution, for the denominator on the RHS (r^2 + 2)... you can multiply this to the top of the LHS. You can do this because r^2 is ALWAYS positive and therefre (r^2 + 2) is always a positive answer.

Is the OA C?

has to be (C)