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

If α and β be two roots of the equation x2-64x+256=0. Then the value of α3β518+β3α518 is :
  1. 2
  2. 3
  3. 1
  4. 4

Solution

Given equation is x2-64x+256=0 whose roots are α, β.

α+β=64, αβ=256
Now α3β518+β3α518
=α38+58+β38+58(αβ)5/8=α+β(αβ)5/8
=64(256)5/8=6432=2

Asked in: JEE Main 2020 (06 Sep Shift 1)

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