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x=√3+1/2
x-1/2=√3
squaring on both sides
(x-1/2)²=3
4x²+1-x=3
4x²-x-2=0......................(1)
take the lhs and divide it by 4xcube +2x² -8x+7
hence
4xcube +2x² -8x + 7= (4x²-x-2)(x+3/4)+(-21/4x+17/2)
from eq (1)
=0(x+3/4) + (-21/4x+17/2)
=-21/4(√3+1/2) + 17/2
=47-42√3 / 8 ans.
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