Question

(x²+2x+3)(3y²+2y+1)=4/3,则x+y=?

Answer 1

(x²+2x+3)(3y²+2y+1)=4/3

(x²+2x+3)=(x+1)^2+2>=2

(3y²+2y+1) = (√3y+1/√3)^2+2/3>=2/3

(x²+2x+3)(3y²+2y+1)>=2*2/3=4/9

因此上面两个不等式刚好取到等式,得

x=-1,y=-1/3

x+y=-4/3