TS EAMCET · Maths · Basic of Mathematics
If \(\alpha\) and \(\beta\) are the least positive integers such that for all \(n \in N, n^3+\alpha n\) is divisible by 3 and \(n^3-\beta n\) is divisible by 6 , then \(\alpha+\beta=\)
- A \(4\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
If for all \(n \in N, n^3+\alpha n\) is divisible by 3 , then for \(n=1\) also it is divisible by 3 , so the least positive integral value of \(\alpha=2\) And, since for all \(n \in N, n^3-\beta n\) is divisible by 6 , then for \(n=1\) also it is divisible by 6 , so the least…
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