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If `x^(2) - x+ 1 =0, sum_(n=1)^(5) (x^(n) +(1)/(x^(n)))` equals -A. 8B. 10C. 12D. 14 |
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Answer» Correct Answer - 1 `x = - omega,- omega^(2) rArr x + (1)/(x) = 1, x^(2) +(1)/(x^(2)) = -1`, `x^(3) + (1)/(x^(3)) = - 2 ,x+(1)/(x^(4)) = -1, x^(5) +(1)/(x^(5))=1` `underset(n=1)overset(5)sum (x^(n)+(1)/(x^(n)))^(2)` `=(1)^(2) +(-1)^(2) +(-2)^(2)+(-1)^(2)+(1)^(2)` `= 1+1+ 4+ 1+1` =8 |
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