Question

椭圆x^2/4+y^2=1上点p(x,y),求(y^2+1/y^2)(x^2/4+4/x^2)的最小值

Answer 1

令x=2sint,y=cost,则(y^2+1/y^2)(x^2/4+4/x^2)=[（cost）^2+1/（cost）^2][（sint）^2+1/（sint）^2]=(sin2t)^2/4+8/(sin2t)^2-2>=2sqt[(sin2t)^2/4+8/(sin2t)^2]-2=2sqt(2)-2

注：sqt指平方根