4a2 + 1/a2 = 2 হয়, তবে 8a3 + 1/a3 এর মান কত?
Solution
Correct Answer: Option A
দেওয়া আছে,
(2a)2 + (1/a)2 = 2
⇒ {2a + (1/a)}2 - 2 . 2a . (1/a) = 2
⇒ {2a + (1/a)}2 = 2 + 4 = 6
⇒ {2a + (1/a)}2 = 6
⇒ 2a + (1/a) = √6
এখন,
8a3 + 1/a3
= (2a)3 + (1/a)3
= {2a + (1/a)} {(2a)2 - 2a. (1/a) + (1/a)2}
= √6 (2 - 2)
= 0
(2a)2 + (1/a)2 = 2
⇒ {2a + (1/a)}2 - 2 . 2a . (1/a) = 2
⇒ {2a + (1/a)}2 = 2 + 4 = 6
⇒ {2a + (1/a)}2 = 6
⇒ 2a + (1/a) = √6
এখন,
8a3 + 1/a3
= (2a)3 + (1/a)3
= {2a + (1/a)} {(2a)2 - 2a. (1/a) + (1/a)2}
= √6 (2 - 2)
= 0
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