Question

已知实数a、b满足等式a^2-2a-1=0,b^2-2b-1=0,求b/a+a/b的值

Answer 1

显然a,b是x^2-2x-1=0的两根

则：a+b=2

ab=-1

(b/a)+(a/b)=(a^2+b^2)/(ab)

=[(a+b)^2-2ab]/(ab)

=[(a+b)^2/(ab)]-2

=(4/(-1))-2

=-6