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

Asked by nisha_vini29 | 23rd Apr, 2015, 11:01: PM

Expert Answer:

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

Answered by Prasenjit Paul | 24th Apr, 2015, 10:23: AM