已知实数x,y,a,b,满足x^2+y^2=1,a^2+b^2=3,则ax+by的最大值是
人气:198 ℃ 时间:2020-01-27 20:59:31
解答
两个不等式相加可能会使范围扩大,解题过程中应避免
(x^2+y^2)(a^2+b^2)=3=a^2x^2+b^2y^2+a^2y^2+b^2x^2≥a^2x^2+b^2y^2+2abxy=(ax+by)^2,也就是3≥(ax+by)^2, 根号3≥ax+by
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