15 Possible values for expression | Summary and Q&A
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TL;DR
Determine the possible value of p minus n given the equation p squared minus n squared is equal to 12.
Key Insights
- ➕ The equation p squared minus n squared can be factored as (p plus n)(p minus n) = 12.
- ➕ Both p plus n and p minus n are positive integers because p is greater than n and both are positive.
- 😀 By considering all possible combinations of positive integers that result in a product of 12, we can determine the potential values for p and n.
Transcript
- [Voiceover] If p and n are integers such that p is greater than n, is greater than zero. So this tells us since p is strictly greater than n that means that they're two different integers. p is larger of these two different integers and that they're both positive. They're both greater than zero and they tell us that p squared minus n squared is e... Read More
Questions & Answers
Q: What is the equation that needs to be solved in this analysis?
The equation that needs to be solved is p squared minus n squared = 12, with the objective of finding the value of p minus n.
Q: How can the equation be simplified?
The equation can be simplified by factorizing p squared minus n squared as (p plus n)(p minus n) = 12.
Q: What condition must be satisfied for p minus n to be a positive value?
For p minus n to be positive, p must be greater than n, as stated in the problem.
Q: How can potential values for p minus n be determined?
By considering all possible combinations of positive integers that multiply to give 12, such as 12 times 1, 6 times 2, and 4 times 3, we can determine potential values for p plus n and p minus n.
Summary & Key Takeaways
-
Given that p is greater than n and both are positive integers, find the potential value of p minus n.
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Factorizing p squared minus n squared leads to (p plus n)(p minus n) = 12.
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Evaluate various combinations of positive integers such as 12 times 1, 6 times 2, and 4 times 3 to determine possible values for p minus n.
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