# Thread: Proving that an inequality holds

1. ## Proving that an inequality holds

Hello,
I do not know if this is the right place to post this question, but I believe it falls under algebra. Please redirect me if appropriate.

Question:

How can I show that $$P-QR^3<\frac{R^4}{C}$$ for $$C,P,Q,R > 0?$$

Thanks.

2. ## Re: Proving that an inequality holds

Originally Posted by abscissa
Hello,
I do not know if this is the right place to post this question, but I believe it falls under algebra. Please redirect me if appropriate.

Question:

How can I show that $$P-QR^3<\frac{R^4}{C}$$ for $$C,P,Q,R > 0?$$

Thanks.
You cannot show it because it is not true.

Example. Let R = 2, C = 4, P = 100, Q = 3

$P - QR^3 = 100 - 3 * 2^3 = 100 - 3 * 8 = 100 - 24 = 76.\ And\ \dfrac{R^4}{C} = \dfrac{2^4}{4} = \dfrac{16}{4} = 4.$

$76 \not < 4.$

There must be additional constraints that you have not specified.

3. ## Re: Proving that an inequality holds

Originally Posted by JeffM
You cannot show it because it is not true.

Example. Let R = 2, C = 4, P = 100, Q = 3

$P - QR^3 = 100 - 3 * 2^3 = 100 - 3 * 8 = 100 - 24 = 76.\ And\ \dfrac{R^4}{C} = \dfrac{2^4}{4} = \dfrac{16}{4} = 4.$

$76 \not < 4.$

There must be additional constraints that you have not specified.
Ok. You are right. Would you mind if I start a new question within this one, one with more context and details? Thanks.

4. ## Re: Proving that an inequality holds

Not a problem. Go right ahead. Someone will be around to help