Finding conditions for which an inequality holds

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SUMMARY

The discussion centers on the inequality condition $$P-QR^3<\frac{R^4}{C}$$ for positive values of $$C, P, Q, R$$. A specific counterexample is provided with values $$P=1000$$, $$Q=2$$, $$R=3$$, and $$C=10000$$, demonstrating that the inequality does not hold true in this case. The conclusion emphasizes that the statement is not universally valid, highlighting the necessity of specific conditions for the inequality to be satisfied.

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kalish1
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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.
 
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That statement is not true in general.
Consider $P=1000$, $Q=2$, $R=3$, $C=10000$, the inequality would be false.
 

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