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题目

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答案

令x=tcosa
y=tsina 1≤t≤√2
x^2-xy+y^2=t2-t^2sinacosa=t^2[1-(1/2)*sin2a]
1/2=1-1/2≤[1-(1/2)*sin2a]≤1+1/2=3/2
1/2≤t^2*(1/2)≤x^2-xy+y^2≤t^2*(3/2)≤3/2
故1/2