If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?
x2 − x + 1 = 0 αβ = 1 α + β =1 cubing on both sides α3 + β3 + 3αβ(α + β) = 1 α3 + β3 + 3 ∗ 1(1 ) = 1 α3 + β3 = -2 α3 β3 = 1 Sum of the roots=-2 product=1 Required equation is x2 + 2x + 1 = 0
64 66 76 126 376 ?
...217 267 304 330 348 357
...147 138 120 93 ? 12
...43 36 50 29 ? 22
...10 625 50 125 250 25 ?
...21 84 168 172 ? 348
...1 2 11 36 85 ?
...7, 26, 238, 962, 8522, 34078
To find the Next number in the given series.
0 6 24 60 120 ?
...32, ?, 41, 68, 132, 257
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