If α and β be two roots of the equation x 2 - 64 x + 256 = 0 . Then the value of α 3 β 5 1 8 + β 3 α 5 1 8 is :

Question

If α and β be two roots of the equation x 2 - 64 x + 256 = 0 . Then the value of α 3 β 5 1 8 + β 3 α 5 1 8 is :, 2, 3, 1, 4

MARKS App · Accepted Answer

Given equation is x 2 - 64 x + 256 = 0 whose roots are α , β . α + β = 64 , α β = 256 Now α 3 β 5 1 8 + β 3 α 5 1 8 = α 3 8 + 5 8 + β 3 8 + 5 8 ( α β ) 5 / 8 = α + β ( α β ) 5 / 8 = 64 ( 256 ) 5 / 8 = 64 32 = 2

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