Question

已知a=1/[(根号3)+1] 求a^3+a^2-4a-7

Answer 1

a=1/(√ 3+1)= (√3-1)/2,

所以2a+1=√3,那么(2a+1)^2=3

a^3+a^2-4a-7=1/4*a(4a^2+4a+1)-1/4a-4a-7=1/4*a*(2a+1)^2-1/4a-4a-7=1/4*a*3-1/4a-4a-7

=7/2*a-7=7/2*(√3-1)/2-7=7/4*√3 -35/4