Question

If x=1/2+underroot 3then find the value of 2xcube-7xsquare-2x-1

Answer 1

4x^3+2x^2–8x+7=? , given x=(3^1/2 +1(/2

=2x(2x^2+x-4)+7

=2x[2x(x+1/2)-4]+7

put x=(3^1/2 +1)/2

=(3^1/2+1)[(3^1/2 +1)(3^1/2 +1+1)/2 -4]+7

=(3^1/2+1)[(3^1/2 +1)(3^1/2 +2)/2 -4]+7

=(3^1/2 +1)[(3+3.3^1/2+2)/2–4]+7

=(3^1/2 +1)[5+3.3^1/2–8]/2 + 7

=(3^1/2 +1)(3.3^1/2–3)/2 +7

=(3/2).(3^1/2+1) (3^1/2 -1)+7

=(3/2)(3–1)+7

=3/2×2/1+7

=3+7