Question
If a+1/a =9, then a5+1/a5 is equal
to:Solution
a + (1/a) = 9 = ( a² + 1/a² ) = (9) ² - 2 = 81 - 2 = 79 (a³ + 1/a³ ) = (a+1/a)3 -3(a+1/a) ⇒ (a³ + 1/a³ ) = (9)3 - (3 x 9) = 729 - 27 = 702 a5+ (1/a5) = (a² + 1/a²) x (a³ + 1/a³) - (a + 1/a) =79 x 702-9 =15134-7 = 55458-7 =55451 The correct answer is 55451.
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