x - 1/x = √3 যেখানে, x≠ 0 হলে, x6 + 1/x6 এর মান কত?
Solution
Correct Answer: Option D
দেওয়া আছে,
x - 1/x = √3
⇒ (x - 1/x)2 = (√3)2
⇒ x2 - 2.x.1/x + (1/x)2=3
∴ x2 + (1/x)2 = 5
এখন, পদত্ত রাশি,
x6 + 1/x6
= (x2)3 + (1/x2)3
= (x2 + 1/x2)3-3.x2.1/x2 (x2 + 1/x2)
= 53 - 3.5
= 125 - 15
= 110
x - 1/x = √3
⇒ (x - 1/x)2 = (√3)2
⇒ x2 - 2.x.1/x + (1/x)2=3
∴ x2 + (1/x)2 = 5
এখন, পদত্ত রাশি,
x6 + 1/x6
= (x2)3 + (1/x2)3
= (x2 + 1/x2)3-3.x2.1/x2 (x2 + 1/x2)
= 53 - 3.5
= 125 - 15
= 110
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