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因為(a2+b2)(c2+d2)-(ac+bd)2=(a2c2+a2d2+b2c2+b2d2)-(a2c2+b2d2+2abcd)=b2c2+a2d2-2abcd=(bc-ad)2≥0又ad≠bc所以(bc-ad)2>0所以(a2+b2)(c2+d2)>(ac+bd)2.
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