# What is the solution?

#### Idea

no, the answer is not $$\displaystyle 2$$

#### MathScience Daniel Dallas

Hi! 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.

Daniel Dallas

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topsquark

#### Lev888

Yeah, you are right!
That is 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
If b and c are 4, bc = 16. This contradicts the problem statement (bc=4).

#### greg1313

(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
You need grouping symbols around the denominator:

(bc + ac + ab)/(abc) = 1/2

But, with bc = ac = ab = 4, and abc = 16, that makes the value of the fraction equal
to 12/16 = 3/4, which is not equal to 1/2.

It is a faulty/impossible problem.

#### MathScience Daniel Dallas

You need grouping symbols around the denominator:

(bc + ac + ab)/(abc) = 1/2

But, with bc = ac = ab = 4, and abc = 16, that makes the value of the fraction equal
to 12/16 = 3/4, which is not equal to 1/2.

It is a faulty/impossible problem.
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.

Daniel Dallas

Last edited by a moderator:
topsquark

$$\displaystyle ab = bc \implies a = c , (b \neq 0)$$
$$\displaystyle bc = ac \implies b = a , (c \neq 0)$$
$$\displaystyle a = b = c$$
$$\displaystyle ab = a^2 = 4 \implies a = 2, -2$$
$$\displaystyle \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{3}{a} = \frac{1}{2} \implies a = 6$$