已知实数a、b、c满足a+b+c=0,a2+b2+c2=6,则a的最大值为______.∵a+b+c=0,∴c=-(a+b),∴a2+b2+[-(a+b)]2=6,∴b2+ab+(a2-3)=0,∴△=a2-4(a2-3)=-3a2+12≥0,解得,-2≤a≤2,∴a的最大值为2.2.其中△ 为什么要>
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![已知实数a、b、c满足a+b+c=0,a2+b2+c2=6,则a的最大值为______.∵a+b+c=0,∴c=-(a+b),∴a2+b2+[-(a+b)]2=6,∴b2+ab+(a2-3)=0,∴△=a2-4(a2-3)=-3a2+12≥0,解得,-2≤a≤2,∴a的最大值为2.2.其中△ 为什么要>](/uploads/image/z/2724463-55-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0a%E3%80%81b%E3%80%81c%E6%BB%A1%E8%B6%B3a%2Bb%2Bc%3D0%2Ca2%2Bb2%2Bc2%3D6%2C%E5%88%99a%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%BA______%EF%BC%8E%E2%88%B5a%2Bb%2Bc%3D0%2C%E2%88%B4c%3D-%EF%BC%88a%2Bb%EF%BC%89%2C%E2%88%B4a2%2Bb2%2B%5B-%EF%BC%88a%2Bb%EF%BC%89%5D2%3D6%2C%E2%88%B4b2%2Bab%2B%EF%BC%88a2-3%EF%BC%89%3D0%2C%E2%88%B4%E2%96%B3%3Da2-4%EF%BC%88a2-3%EF%BC%89%3D-3a2%2B12%E2%89%A50%2C%E8%A7%A3%E5%BE%97%2C-2%E2%89%A4a%E2%89%A42%2C%E2%88%B4a%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%BA2%EF%BC%8E2%EF%BC%8E%E5%85%B6%E4%B8%AD%E2%96%B3+%E4%B8%BA%E4%BB%80%E4%B9%88%E8%A6%81%3E)
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