Question

先化简,再求值:[(a^2-4)\(a^2-4a+4)-a/(2-a)]÷2/(a^2-2a),其中,a是方程x^2+3

Answer 1

[(a^2-4)/(a^2-4a+4)-a/(2-a)]÷[2/(a^2-2a)]

=[(a+2)(a-2)/(a-2)^2-a/(2-a)]*[(a^2-2a)/2]

=[(a+2)/(a-2)-a/(2-a)]*[(a^2-2a)/2]

=[2/(a-2)]*[a(a-2)/2]

=a

a是方程x^2+3x+1=0的解,

a^2+3a+1=0,

a=(-3±√5)/2

a^2+3a+1=0

a^2+2(3/2)a+(3/2)^2+1-9/4=0

(a+3/2)^2=5/4

a+3/2=±√5/2

a=-3/2±√5/2