MHB Finding conditions for which an inequality holds

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The discussion centers on the inequality P - QR^3 < R^4/C for positive values of C, P, Q, and R. It is pointed out that the inequality does not hold universally, providing a counterexample with specific values: P=1000, Q=2, R=3, and C=10000. The counterexample demonstrates that the inequality can be false under certain conditions. Participants are encouraged to explore the conditions under which the inequality might hold true. The conversation emphasizes the need for careful consideration of variable values in algebraic inequalities.
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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