Question
Solution
x + 1/x = 2√2 Taking cube on both sides,          (a + b)3 = a3 + 3a2 b + 3ab2 + b3 x3+1/x 3+ 3×x2×1/x + 3x × 1/x2 = (2√2)3  x3+1/x 3 + 3(x+1/x) =16√2 x3+1/x 3 + 3(2√2) =16√2 x3+1/x 3 =16√2-6√2=10√2             … (1) if x + 1/x = 2√2 then x-1/x =2 x3-1/x3 =8+6 x3-1/x3 = 14              … (2) x6-1/x6 =( x3+1/x 3)( x3-1/x3) =10√2 ×14 =140√2
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