If n3 is odd, which of the following statements are true?

If \(n^{3}\) is odd, which of the following statements are true? ?

Created: 1 week ago | Updated: 1 week ago | Created By:

Imran Ahmed

I only

II only

III only

I and II only

0 1

Best Answer Explained in Below-:

ধরি, \(n^{3}\) একটি odd integer তাহলে \(n^{3}\) কে 2K + 1 হিসেবে প্রকাশ করা যায়, যেখানে k যে কোনো integer \(n^{3}\) = 2k + 1⇒\(n^{3}\) - 1 = 2k⇒n - 1n2 + n + 1 = 2k⇒n - 1nn + 1 + 1 = 2k যেহেতু ডানপাশে 2k তাহলে বামপাশের দুটি Factor multiply করে একটি even number গঠন করবে।এখানে n(n + 1) সবসময় even যেহেতু দুটি consecutive terms product even, এর যেমন - 2×3 = 6 এর সাথে 1 যোগ মানে odd. তাহলে (n - 1) নিশ্চয়ই even কেননা (n - 1) এবং {n(n + 1) + 1}এর গুণফল even;odd এবং odd এর গুণফল even হতে পারে না।(n - 1) even মানে n odd । আবার odd সংখ্যার সাথে odd গুণফল এর odd অর্থাৎ n2odd ।

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If \(n^{3}\) is odd, which of the following statements are true? ?

For how many positive numbers a, it becomes true that a * a * a = a + a + a ?

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