已知a,b,c为实数,且ab/(a+b)=1/3,bc/(b+c)=1/4,ac/(a+c)=1/5,求abc/(ab+bc+ac)的值
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已知a,b,c为实数,且ab/(a+b)=1/3,bc/(b+c)=1/4,ac/(a+c)=1/5,求abc/(ab+bc+ac)的值
已知a,b,c为实数,且ab/(a+b)=1/3,bc/(b+c)=1/4,ac/(a+c)=1/5,求abc/(ab+bc+ac)的值
已知a,b,c为实数,且ab/(a+b)=1/3,bc/(b+c)=1/4,ac/(a+c)=1/5,求abc/(ab+bc+ac)的值
已知的分别倒数后1/a+1/b=3 1/b+1/c=4 1/a+1/c=5
三式相加除以2得:1/a+1/b+1/c=6
abc/(ab+bc+ac)=1/(1/c+1/b+1/a)=1/6
1/6
1/6
1/6
应是
已知a、b、c为实数,且ab/a+b=1/3,bc/a+c=1/4,ac/a+c=1/5,那么abc/ab+bc+ac的值是多少?
因为 ab/(a+b)=1/3 , bc/(b+c)=1/4 , ca/(c+a)=1/5
所以:
(a+b)/ab = 3
(b+c)/bc = 4
(a+c)/ac = 5
即:
1...
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应是
已知a、b、c为实数,且ab/a+b=1/3,bc/a+c=1/4,ac/a+c=1/5,那么abc/ab+bc+ac的值是多少?
因为 ab/(a+b)=1/3 , bc/(b+c)=1/4 , ca/(c+a)=1/5
所以:
(a+b)/ab = 3
(b+c)/bc = 4
(a+c)/ac = 5
即:
1/a + 1/b = 3
1/b + 1/c = 4
1/a + 1/c = 5
三式相加,得:
2(1/a + 1/b + 1/c) = 12
所以:1/a + 1/b + 1/c = 6
1/a + 1/b + 1/c
=(ab+bc+ca)/abc
=(ab+bc+ca)/abc
= 6
取倒数:abc/(ab+bc+ca) = 1/6
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