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
14, 17, 23, 32, ?, 59
32, 64, 8, ?, 2, 4Â
9 19 39 ? 159 319
18   29   16   31   ?   33
13, 29, 65, 129, ?, 373
47, 72, 122, ?, 297, 422
What will come in place of the question mark (?) in the following series?
24, 8, 15, ?, 12, 4
12, 18, 30, 54, ?, 198
What will come in place of the question mark (?) in the following series?
9, 22, 61, ?, 217, 334
4, 7, 12, 21, 36, ?
