x+(1/x)=√3 হলে x3+ (1/x3) এর মান কত?

 

A 2

B 4

D 6

Solution

Correct Answer: Option C

দেওয়া আছে, x+(1/x)=√3

⇒ {x+(1/x)}2=(√3)2
⇒ x2 + 2 . x . (1/x) + (1/x2) = 3
⇒  x2 + (1/x2) = 3 - 2 = 1
⇒  x2 + (1/x2) = 1

এখন, (x3+1/x3)
= (x)3 + (1/x)3
= {x + (1/x)} {x2 - x . (1/x) + (1/x)2}
= (√3) {x2 + (1/x2) - 1}
= (√3) (1 - 1)
= 0 

বিকল্প সমাধানঃ
দেওয়া আছে, x+(1/x)=√3

এখন,
(x3+1/x3) = (x + 1/x)3 -3.x.1/x(x + 1/x)
               =(√3)3 - 3√3
               = 3√3 - 3√3
               = 0

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