若a、b、c、d是四个正数,且abcd=1.求(a/abc+ab+a+1)+(b/bcd+bc+b+1)+(c/cda+
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/06/22 22:11:28
若a、b、c、d是四个正数,且abcd=1.求(a/abc+ab+a+1)+(b/bcd+bc+b+1)+(c/cda+cd+c+1)+(d/dab+da+d+1)的值
![若a、b、c、d是四个正数,且abcd=1.求(a/abc+ab+a+1)+(b/bcd+bc+b+1)+(c/cda+](/uploads/image/z/4789481-41-1.jpg?t=%E8%8B%A5a%E3%80%81b%E3%80%81c%E3%80%81d%E6%98%AF%E5%9B%9B%E4%B8%AA%E6%AD%A3%E6%95%B0%2C%E4%B8%94abcd%3D1.%E6%B1%82%28a%2Fabc%2Bab%2Ba%2B1%29%2B%28b%2Fbcd%2Bbc%2Bb%2B1%29%2B%28c%2Fcda%2B)
a/(abc+ab+a+1)+b/(bcd+bc+b+1)+c/(cda+cd+c+1)+d/(dab+da+d+1)
=a/(1/d+ab+a+1)+b/(bcd+bc+b+1)+c/(1/b+cd+c+1)+d/(dab+da+d+1)
=ad/(abd+ad+d+1)+b/(bcd+bc+b+1)+bc/(bcd+bc+b+1)+d/(dab+da+d+1)
=(ad+d)/(abd+ad+d+1)+(b+bc)/(bcd+bc+b+1)
=(ad+d)/(abd+ad+d+abcd)+(b+bc)/(bcd+bc+b+abcd)
=(a+1)/(ab+a+1+abc)+(1+c)/(cd+c+1+acd)
=(a+1)/[(a+1)+ab(c+1)]+(c+1)/[(c+1)+cd(a+1)]
=1/[1+ab(c+1)/(a+1)]+1/[1+cd(a+1)/(c+1)]
=1/{1+(c+1)/[cd(a+1)]}+1/[1+cd(a+1)/(c+1)]
令(c+1)/[cd(a+1)]=x
则cd(a+1)/(c+1)=1/x
所以原式=1/(1+x)+1/(1+1/x)
=1/(1+x)+x/(1+x)
=(1+x)/(1+x)
=1
=a/(1/d+ab+a+1)+b/(bcd+bc+b+1)+c/(1/b+cd+c+1)+d/(dab+da+d+1)
=ad/(abd+ad+d+1)+b/(bcd+bc+b+1)+bc/(bcd+bc+b+1)+d/(dab+da+d+1)
=(ad+d)/(abd+ad+d+1)+(b+bc)/(bcd+bc+b+1)
=(ad+d)/(abd+ad+d+abcd)+(b+bc)/(bcd+bc+b+abcd)
=(a+1)/(ab+a+1+abc)+(1+c)/(cd+c+1+acd)
=(a+1)/[(a+1)+ab(c+1)]+(c+1)/[(c+1)+cd(a+1)]
=1/[1+ab(c+1)/(a+1)]+1/[1+cd(a+1)/(c+1)]
=1/{1+(c+1)/[cd(a+1)]}+1/[1+cd(a+1)/(c+1)]
令(c+1)/[cd(a+1)]=x
则cd(a+1)/(c+1)=1/x
所以原式=1/(1+x)+1/(1+1/x)
=1/(1+x)+x/(1+x)
=(1+x)/(1+x)
=1
若a、b、c、d是四个正数,且abcd=1.求(a/abc+ab+a+1)+(b/bcd+bc+b+1)+(c/cda+
已知abcd=1,求a/(abc+ab+a+1)+b/(bcd+bc+b+1)+c/(cda+cd+c+1)+d/(da
分式设abcd=1,则a/(abc+ab+a+1)+b/(bcd+bc+b+1)+c/(cda+cd+c+1)+d/(d
证明(abc+bcd+cda+dab)^2-(ab-cd)(bc-da)(ca-bd)=abcd(a+b+c+d)^2
abcd+abc+bcd+cda+dab+ab+bc+cd+da+ac+bd+a+b+c+d=2009 a+b+c+d=
已知abcd=1求1/(abc+ab+a+1)+1/(bcd+bc+b+1)+1/(cda+cd+c+1)+1/(dab
已知abcd=1,求ax/(abc+ab+a+1)+bx/(bcd+bc+b+1)+cx/(cda+cd+c+1)+dx
abcd=1 求1+a+ab+abc分之1 + 1+b+bc+bcd分之1 + 1+d+cd+cda分之1 + 1+d+
已知三个正数a、b、c,满足abc=1.求(a/ab+a+1 )+(b/bc+b+1)+(c/ac+c+1)
若整数a、b、c、d满足1《a《b《c《d《2007,且a+b+c+d=ad+bc,求abcd的最大值与最小值
已知a,b,c,d均为正数,且ab-bc=1,a^2+b^2+c^2+d^2-ab+cd=1,求abcd的值
已知a,b,c是正数,且ab+bc+ca=1,求证:a+b+c>=根3