作业帮证明 (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
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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