ab/a+b=1/6 ,bc/b+c=1/8,ac/a+c=1/10,求abc/ab+bc+ac的值.

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 23:22:18
ab/a+b=1/6 ,bc/b+c=1/8,ac/a+c=1/10,求abc/ab+bc+ac的值.

ab/a+b=1/6 ,bc/b+c=1/8,ac/a+c=1/10,求abc/ab+bc+ac的值.
ab/a+b=1/6 ,bc/b+c=1/8,ac/a+c=1/10,求abc/ab+bc+ac的值.

ab/a+b=1/6 ,bc/b+c=1/8,ac/a+c=1/10,求abc/ab+bc+ac的值.
ab/(a+b)=1/6, (a+b)/ab=6
bc/(b+c)=1/8, (b+c)/bc=8
ca/(c+a)=1/10, (c+a)/ca=10
(a+b)/ab+(b+c)/bc+(c+a)/ca=10+8+6=24
[c(a+b)+a(b+c)+b(c+a)]/abc=24
(ab+bc+ca)/abc=12
abc/(ab+bc+ca)=1/12

ab/(a+b)=1/6,取倒数后为:(a+b)/ab=6,1/b+1/a=6;(1)
同理:bc/(b+c)=1/8, (b+c)/bc=8,1/c+1/b=8;(2)
ac/(a+c)=1/10,(a+c)/ac=10,1/c+1/a=10.(3)
(1)+(2)+(3),得:2(1/a+1/b+1/c)=24, 1/a+1/b+1/c=12,(ab+bc+ca)/abc=12;
abc/(ab+bc+ca)=1/12.

因为 ab/(a+b)=1/6 , bc/(b+c)=1/8 , ca/(c+a)=1/10
所以: (a+b)/ab = 6 (b+c)/bc = 8 (a+c)/ac = 10
即: 1/a + 1/b = 6 1/b + 1/c = 8 1/a + 1/c = 10
三式相加,得: 2(1/a + 1/b + 1/c) = 24
...

全部展开

因为 ab/(a+b)=1/6 , bc/(b+c)=1/8 , ca/(c+a)=1/10
所以: (a+b)/ab = 6 (b+c)/bc = 8 (a+c)/ac = 10
即: 1/a + 1/b = 6 1/b + 1/c = 8 1/a + 1/c = 10
三式相加,得: 2(1/a + 1/b + 1/c) = 24
所以:1/a + 1/b + 1/c = 12
先求“abc/(ab+bc+ca)”的倒数: (ab+bc+ca)/abc = 1/a + 1/b + 1/c = 12
所以: abc/(ab+bc+ca) = 1/12

收起