数学题，急急急用

显示全部楼层 · 2010-8-23 17:53:40

a：b＝c：d，a b c d 均为正数求证： {a3:b+b3:a}:{c3:d+d3:c}=ab:cd

千问 · 2010-8-23 17:53:40

解：∵a b c d 均为正数，a:b＝c:d∴a2:b2=c2:d2，b:a=d:c∴b2:a2=d2:c2∴(a2:b2)+(b2:a2)=(c2:d2)+(d2:c2)∴[(a3:b):ab]+[(b3:a):ab]=[(c3:d):cd]+[(d3:c):cd]∴[(a3:b)+(b3:a)]:ab=[(c3:d)+(d3:c)]:cd∴[(a3:b)+(b3: