TS EAMCET · Maths · Basic of Mathematics
\(x^n+y^n\) is divisible by
- A \(x-y\) for all \(n \in N\)
- B \(x+y\) for all \(n \in N\)
- C \(x+y\) for all \(n=2 m-1, m \in N\)
- D \(x+y\) for all \(n=2 m, m \in N\)
Answer & Solution
Correct Answer
(C) \(x+y\) for all \(n=2 m-1, m \in N\)
Step-by-step Solution
Detailed explanation
Given, \(x^n+y^n\) At \(n=1, x+y\), which is divisible by \(x+y\). \(n=2, x^2+y^2\), which is not divisible by \(x+y\). \(n=3, x^3+y^3\), which is divisible by \(x+y\). Hence, clearly \(x^n+y^n\) is divisible by \(n=\) odd numbers as \(n=2 m-1\), where \(M \in N\).
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