证明 (4 14:50:58)证明(1)已知a>b>0, c<d<0, e<0,求证e/(a-c)>e/(d-b)(2)若x+y+z=a,求证x2+y2+z2≥ a2/3
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![证明 (4 14:50:58)证明(1)已知a>b>0, c<d<0, e<0,求证e/(a-c)>e/(d-b)(2)若x+y+z=a,求证x2+y2+z2≥ a2/3](/uploads/image/z/122084-44-4.jpg?t=%E8%AF%81%E6%98%8E+%284+14%3A50%3A58%29%E8%AF%81%E6%98%8E%EF%BC%881%EF%BC%89%E5%B7%B2%E7%9F%A5a%EF%BC%9Eb%EF%BC%9E0%2C%26%23160%3B+c%EF%BC%9Cd%EF%BC%9C0%2C%26%23160%3B+e%EF%BC%9C0%2C%E6%B1%82%E8%AF%81e%2F%28a-c%29%EF%BC%9Ee%2F%28d-b%29%282%29%E8%8B%A5x%2By%2Bz%3Da%2C%E6%B1%82%E8%AF%81x2%2By2%2Bz2%E2%89%A5%26%23160%3B+a2%2F3)
证明 (4 14:50:58)证明(1)已知a>b>0, c<d<0, e<0,求证e/(a-c)>e/(d-b)(2)若x+y+z=a,求证x2+y2+z2≥ a2/3
证明 (4 14:50:58)
证明(1)已知a>b>0, c<d<0, e<0,求证e/(a-c)>e/(d-b)
(2)若x+y+z=a,求证x2+y2+z2≥ a2/3
证明 (4 14:50:58)证明(1)已知a>b>0, c<d<0, e<0,求证e/(a-c)>e/(d-b)(2)若x+y+z=a,求证x2+y2+z2≥ a2/3
1、
由于a>b>0>d>c,所以a-c>0,d-b
(1)是个错题,如3>2>0,-2<-1<0,-1<0,则-1/(3+2)<-1/(-1-2)
1.
c<d<0→-c>-d>0,又a>b>0,
两边相加得a-c>b-d>0,
→0<1/(a-c)<1/(b-d),
→1/(a-c)-1/(d-b)<0,又因 e<0
→e/(a-c)-e/(d-b)>0,
→e/(a-c)>e/(d-b).
2.
x^2+y^2+z^2=(x+y+z)^2-2xy-2yz-2xz
=...
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1.
c<d<0→-c>-d>0,又a>b>0,
两边相加得a-c>b-d>0,
→0<1/(a-c)<1/(b-d),
→1/(a-c)-1/(d-b)<0,又因 e<0
→e/(a-c)-e/(d-b)>0,
→e/(a-c)>e/(d-b).
2.
x^2+y^2+z^2=(x+y+z)^2-2xy-2yz-2xz
=a^2-2xy-2yz-2xz
≥a^2-(x^2+y^2)-(y^2+z^2)-(x^2+z^2)
= a^2-2(x^2+y^2+z^2)
3(x^2+y^2+z^2)≥a^2
x^2+y^2+z^2≥(a^2)/3
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