Question

若a=(2+根号3)右上角-1 b=(2-根号3)右上角-1,则(a+1)右上角-2+(b+1)右上角-2的值是多少是

Answer 1

a=1/(2+√3) b=1/(2-√3)

∵ab=1/(4-3)=1

∴a=1/b (既a,b互为倒数)

等量代换 式1/(a+1)^2+1/(b+1)^2=1/[(1/b+1)^2]+1/(b+1)^2

=b^2/(b+1)^2+1/(b+1)^2

=(b^2+1)/(b+1)^2

分子,分母同时除以b^2得

=(1+1/b^2)/(1+1/b)^2

将 1/b=2-√3代入得

=[1+(2-√3)^2]/[1+2-√3]^2

=(1+7-4√3)/(12-6√3)

=(8-4√3)/(12-6√3)

=4(2-√3)/6(2-√3)

=2/3

该式的计算结果是2/3