Question
If x + 1/x = 5 then find out the value of x⁵ +
1/(x⁵)?Solution
If x + (1/x) = 5 Then x2 + 1/x2 = 23 and x3 + 1/x3 = 110 so x5 + 1/x5 = (x2 +1/x2) (x3 +1/x3) - (x + 1/x) x5 + 1/x5 = (23 × 110) - (5) => 2530 - 5 = 2525 Formula used: If x + 1/x = a x2 +1/x2 = a²- 2 x + 1/x = a x3 +1/x3 = a³ - 3a
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