Question
Thu April 23, 2015 By: Nisha_vini29

if x=1/2+sqroot3, evaluate 2x3-7x2-2x+1

Expert Reply
Prasenjit Paul
Fri April 24, 2015
x equals fraction numerator 1 over denominator 2 plus square root of 3 end fraction rightwards double arrow x equals fraction numerator 1 left parenthesis 2 minus square root of 3 right parenthesis over denominator left parenthesis 2 plus square root of 3 right parenthesis left parenthesis 2 minus square root of 3 right parenthesis end fraction rightwards double arrow x equals fraction numerator left parenthesis 2 minus square root of 3 right parenthesis over denominator 4 minus 3 end fraction therefore x equals 2 minus square root of 3 x minus 2 equals negative square root of 3 x squared minus 4 x plus 4 equals 3 x squared minus 4 x plus 1 equals 0........ left parenthesis i right parenthesis therefore 2 x cubed minus 7 x squared minus 2 x plus 1 equals 2 x cubed minus 8 x squared plus x squared minus 4 x plus 2 x plus 1 equals 2 x cubed minus 8 x squared plus 2 x plus left parenthesis x squared minus 4 x plus 1 right parenthesis equals 2 x cubed minus 8 x squared plus 2 x plus 0 left square bracket F r o m space left parenthesis i right parenthesis right square bracket equals 2 x open parentheses x squared minus 4 x plus 1 close parentheses equals 2 x cross times 0 equals 0 therefore 2 x cubed minus 7 x squared minus 2 x plus 1 equals 0
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