how to do this question

x=(√3+1)/2

find value of 4x^3-2x^2-8x+7

Asked by ansh123 | 29th Jun, 2018, 12:09: PM

Expert Answer:

begin mathsize 16px style We space have comma
straight x space equals space fraction numerator square root of 3 space plus space 1 over denominator 2 end fraction space space.... left parenthesis 1 right parenthesis
rightwards double arrow 2 straight x space equals space square root of 3 space plus space 1
rightwards double arrow left parenthesis space 2 straight x space minus space 1 right parenthesis space equals square root of 3 space.... left parenthesis 2 right parenthesis

Squaring space on space both space the space sides comma space we space get
left parenthesis space 2 straight x space minus space 1 right parenthesis squared space equals 3
rightwards double arrow 4 straight x squared space minus space 4 straight x space plus 1 space equals space 3
rightwards double arrow 4 straight x squared space minus space 4 straight x space minus 2 space equals space 0 space space space space.... left parenthesis 3 right parenthesis
rightwards double arrow 2 straight x squared minus space 2 straight x space minus 1 space equals space 0 space space
rightwards double arrow 2 straight x squared space equals space 2 straight x space plus space 1 space space space space.... left parenthesis 4 right parenthesis
To space finde space colon space 4 straight x cubed plus space 2 straight x squared space minus space 8 straight x space plus space 7 space equals space ?
4 straight x cubed space minus space 2 straight x squared space minus space 8 straight x space plus space 7 space space space space.... left parenthesis 5 right parenthesis
equals 2 straight x squared left parenthesis space 2 straight x space plus space 1 right parenthesis space minus space 8 straight x space plus space 7
equals left parenthesis space 2 straight x space plus space 1 right parenthesis squared space minus 8 straight x space plus space 7 space...... from space left parenthesis 4 right parenthesis
equals 4 straight x squared space plus space 4 straight x space plus space 1 space minus 8 straight x space plus space 7
equals space 4 straight x squared space minus space 4 straight x space plus space 8
equals space 2 space plus space 8 space space space space space.... from space left parenthesis 3 right parenthesis
equals space 10


space
end style

Answered by Yasmeen Khan | 29th Jun, 2018, 03:10: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.