Question

设正实数x,y满足x2-xy+y2=1,求x2-y2的最大值和最小值

Answer 1

令：x=a+b,y=a-b

x^2-xy+y^2-1=0 ==> a^2+3*b^2=1,a=sinT,b=(√3)(cosT)/3

x^2-y^2 =4ab =(2√3)(sin2T)/3 >0

因此：最小值 0=