Question

若实数a、b满足a分之b+b分之a=2,则a²+4ab+b²分之a²+ab+b²

Answer 1

由b/a+a/b=2,(a^2+b^2)/(ab)=2,a^2+b^2=2ab,(a^2+ab+b^2)/(a^2+4ab+b^2)=(2ab+ab)/(2ab+4ab)=3ab/(6ab)=1/2