What Are the Possible Values of p Minus n?

TL;DR

The only possible value for p minus n given the equation p squared minus n squared equals 12, with p and n as positive integers and p greater than n, is 2. This is determined by factoring the equation into (p plus n)(p minus n) and evaluating the integer combinations that can yield a product of 12.

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

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.

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.

• Factorizing p squared minus n squared leads to (p plus n)(p minus n) = 12.

• 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.