Question

若正数a.b满足a^2/(a^4+a^2+1)=1/24,b^3/(b^6+b^3+1)=1/19,则ab/(a^2+a

Answer 1

因为,a^2/(a^4+a^2+1)=1/24所以,24=(a^4+a^2+1)/a^2=a^2+1+1/a^2=(a+1/a)^2-1由于a>0 所以,a+1/a=√(24+1)=5又因为b^3/(b^6+b^3+1)=1/19所以,19=b^3+1+1/b^3令t=b+1/b可知,t≥2且有,t^3=b^3+3b+3/b+1/b^3=b^3+1+1/b^...