若正数a,b满足aˆ2/(aˆ4+aˆ2+1)=1/24,bˆ3/(bˆ6+bˆ3+1)=1/19,
问题描述:
若正数a,b满足aˆ2/(aˆ4+aˆ2+1)=1/24,bˆ3/(bˆ6+bˆ3+1)=1/19,
则ab/(a^2+a+1)(b^2+b+1)=(),
+
答
因为aˆ2/(aˆ4+aˆ2+1)=1/24,(aˆ4+aˆ2+1)/a^2=24,a^2+2+(1/a)^2=25,(a+1/a)^2=25a+1/a=5bˆ3/(bˆ6+bˆ3+1)=1/19,b^3+1+(1/b)^3=19,(b+1/b)(b^2-1+1/b^2)=18,(b+1/b)((b+1/b...b+1/b=3,这个式子是怎么来的设b+1/b=x,x^3-3x=18 x=3