p=r

Hi

You are making classic mistake of assuming p > 0 when working with this inequality.


1/p > r /r^2 +2
the question is asking:
r^2 +2 > pr ?? ----> Only if p > 0 if p < 0 then r^2 + 2 < pr.. When you cross multiply for inequalities the inequality sign remains as it is when +ve and reverses when you cross multiply with -ve number
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Henc IMO C

IMO - C

Salotuin same as above

C for me too...

uptowngirl92 wrote:1/p > r /r^2 +2

This is how you shud attack these beasts.

Simplify (1/p) - (r/r^2+2)
(r^2+2-pr)/[p(r^2+2)]

A = p(r^2 + 2 - pr), is A > 0

1. p = r
2. r > 0


1. p = r, A = 2p. Whether A is positive or not depends upon whether p is +ve or not, which we dont know. Insufficient.

2. r > 0, we cant determine A's sign using just r.

Combining together A = 2p = 2r > 0. Sufficient.

I solve this by picking numbers, although not the best way. I didn't simplify because I made a rule for myself after making many mistakes:

If there are two variables on different sides of inequality, the only time I can cross multiply or divide each side by one of the variables, if I know that both variables are positive or both are negative.

Please tell me if I am wrong, and if I need to adjust this rule.

fo example: if there is w^3 > w^2 I can't divide each side by w.

heshamelaziry wrote:I solve this by picking numbers, although not the best way. I didn't simplify because I made a rule for myself after making many mistakes:

If there are two variables on different sides of inequality, the only time I can cross multiply or divide each side by one of the variables, if I know that both variables are positive or both are negative.

Please tell me if I am wrong, and if I need to adjust this rule.

fo example: if there is w^3 > w^2 I can't divide each side by w.

w^3 > w^2

Just make sure about the sign of the number you are dividing.

for instance, w^2 is +ve whetehr w is +ve or -ve.

Therfore, w > 1.

w^4 > w^3

Here, you can't divide by w^3. Just divide by w^2.

You are left with: w^2 > w