Question

先化简在求值（a^2-4a+4分之a^2-4—2-a分之1）÷a^2-2a分之2,其中a是方程x^2+3x-6的根.

Answer 1

a是方程x^2+3x-6的根

则有a^2+3a-6=0

a^2+3a=6

（a^2-4a+4分之a^2-4—2-a分之1）÷a^2-2a分之2

=（ (a+2)(a-2)/(a-2)^2 +1/(a-2)）*(a^2-2a)/2

=（ (a+2)/(a-2) +1/(a-2)）*a(a-2)/2

= (a+3)/(a-2) *a(a-2)/2

= a(a+3)/2

= (a^2+3a)/2

=6/2

=3