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What is the compleate solution? I can't solve.
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Try to get a common denominator and show us your work
Do you know what the common denominator would be?
 
This problem is very strange. I am embarrassed that not only can I not do this problem but I do not see any errors in my work.

Here goes: 1a+1b+1c=4abc+4abc+4abc=12abc=12soabc=24\displaystyle \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = \dfrac{4}{abc} + \dfrac{4}{abc} + \dfrac{4}{abc} = \dfrac{12}{abc} = \dfrac{1}{2} \\ so \\abc =24

Since ab=4\displaystyle ab = 4, we get c=6\displaystyle c=6 But ac=4\displaystyle ac = 4 so b=6\displaystyle b=6 (similarly we get a=6\displaystyle a=6). But this contradicts ab=ac=bc=4\displaystyle ab =ac=bc = 4

2nd method. abc=24\displaystyle abc=24 Now abbc=ac=1\displaystyle \dfrac{ab}{bc}=\dfrac{a}{c} = 1 So a=c\displaystyle a=c Same argument that b=c\displaystyle b=c so a=b=c\displaystyle a=b=c. This yields that a=b=c=2\displaystyle a=b=c=2 (assuming positive numbers). Then we get 12+12+12=12\displaystyle \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} =\dfrac{1}{2} which is also not true.

Now if a, b and c were all -2, then the sum would not be 1/2. If only one was -2 and the others both 2, than that would contradict that the product of any 2 would be 4.

What is going on here?
 
This problem is very strange. I am embarrassed that not only can I not do this problem but I do not see any errors in my work.

Here goes: 1a+1b+1c=4abc+4abc+4abc=12abc=12soabc=24\displaystyle \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = \dfrac{4}{abc} + \dfrac{4}{abc} + \dfrac{4}{abc} = \dfrac{12}{abc} = \dfrac{1}{2} \\ so \\abc =24

Since ab=4\displaystyle ab = 4, we get c=6\displaystyle c=6 But
It is ok with that.

Try to have a look at my solution

Hi! Common Denominator: (bc+ac+ab)/abc=1/2
Next abc=16 and a=4/b so c=4 then if a=4/c then a=1 and b=4. So the answer is 1+4+4=9

Your Youtuber,
Math Science by Daniel Dallas


MATHScience Daniel Dallas, you're incorrect. greg1313 explained how you are wrong in the Math Help Forum about this.

This problem is faulty/impossible.
 
Common Denominator: (bc+ac+ab)/abc=1/2
Next abc=24 . However if You express abc through initial conditions like a=4/b, b=4/c and c=4/a and multiply abc you will have that abc=64/(abc) from where abc=+-8, wich is a contradiction to original statement about abc=24.

Your Youtuber,
Math Science by Daniel Dallas
 
This problem is very strange. I am embarrassed that not only can I not do this problem but I do not see any errors in my work.

Here goes: 1a+1b+1c=4abc+4abc+4abc=12abc=12soabc=24\displaystyle \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = \dfrac{4}{abc} + \dfrac{4}{abc} + \dfrac{4}{abc} = \dfrac{12}{abc} = \dfrac{1}{2} \\ so \\abc =24

Since ab=4\displaystyle ab = 4, we get c=6\displaystyle c=6 But ac=4\displaystyle ac = 4 so b=6\displaystyle b=6 (similarly we get a=6\displaystyle a=6). But this contradicts ab=ac=bc=4\displaystyle ab =ac=bc = 4

2nd method. abc=24\displaystyle abc=24 Now abbc=ac=1\displaystyle \dfrac{ab}{bc}=\dfrac{a}{c} = 1 So a=c\displaystyle a=c Same argument that b=c\displaystyle b=c so a=b=c\displaystyle a=b=c. This yields that a=b=c=2\displaystyle a=b=c=2 (assuming positive numbers). Then we get 12+12+12=12\displaystyle \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} =\dfrac{1}{2} which is also not true.

Now if a, b and c were all -2, then the sum would not be 1/2. If only one was -2 and the others both 2, than that would contradict that the product of any 2 would be 4.

What is going on here?
Strange is correct

abc = 64\displaystyle \sqrt{64} = 8

Here goes: 1a+1b+1c\displaystyle \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}

\(\displaystyle = \dfrac{bc + ab + ca}{abc}

= \dfrac{3*4}{abc} = \dfrac{12}{8} \ \ne {\frac{1}{2}}\)......................... The given value

So the problem cannot be solved as posted.
 
Strange is correct

abc = 64\displaystyle \sqrt{64} = 8

Here goes: 1a+1b+1c\displaystyle \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}

\(\displaystyle = \dfrac{bc + ab + ca}{abc}

= \dfrac{3*4}{abc} = \dfrac{12}{8} \ \ne {\frac{1}{2}}\)......................... The given value

So the problem cannot be solved as posted.
How are you getting abc=8?
 
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