Evaluate 2012+((a - b)(b - c)(c - a))/(abc)

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In summary, the equation "Evaluate 2012+((a - b)(b - c)(c - a))/(abc)" is used to evaluate the value of a mathematical expression with variables "a", "b", and "c". It can be applied in real life situations such as population growth or financial analysis. The variables can take on any real number as their value, but certain combinations may result in undefined answers. There is an alternate form of the equation, and it can be solved by substituting values for the variables and using the order of operations or by using a scientific calculator or computer program.
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anemone
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If $a, b, c$ are real numbers with $\dfrac{a-b}{c}+\dfrac{b-c}{a}+\dfrac{c-a}{b}=36$, evaluate $\dfrac{(a-b)(b-c)(c-a)}{abc}+2012$.
 
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Re: Evaluate 2012+((a-b)(b-c)(c-a))/abc

My solution
It interesting that $\dfrac{a-b}{c} + \dfrac{b-c}{a} + \dfrac{c-a}{b} = -\dfrac{(a-b)(b-c)(c-a)}{abc}$ so adding the constraint to the given expression to be evaluated gives $1976$.
 
  • #3
Re: Evaluate 2012+((a-b)(b-c)(c-a))/abc

Jester said:
My solution
It interesting that $\dfrac{a-b}{c} + \dfrac{b-c}{a} + \dfrac{c-a}{b} = -\dfrac{(a-b)(b-c)(c-a)}{abc}$ so adding the constraint to the given expression to be evaluated gives $1976$.

Thanks for participating and well done, Jester!

Yes, it took me some time to realize $\dfrac{a-b}{c} + \dfrac{b-c}{a} + \dfrac{c-a}{b} = -\dfrac{(a-b)(b-c)(c-a)}{abc}$! :eek:
 

FAQ: Evaluate 2012+((a - b)(b - c)(c - a))/(abc)

What is the purpose of the equation "Evaluate 2012+((a - b)(b - c)(c - a))/(abc)"?

The equation is used to evaluate the value of a mathematical expression, where "a", "b", and "c" are variables that represent numbers. The expression is calculated by subtracting "b" from "a", then multiplying that result by "b" minus "c", and finally multiplying that result by "c" minus "a". This value is then divided by the product of "a", "b", and "c", and added to the number 2012.

How can this equation be applied in real life?

This equation can be applied in various situations, such as calculating the growth rate of a population or the change in temperature over time. It can also be used in financial analysis, for example, to determine the return on investment or to predict future trends.

What are the possible values of the variables "a", "b", and "c" in this equation?

The variables can take on any real number as their value. However, it is important to note that certain combinations of values may result in undefined answers, such as when "a", "b", and "c" are all equal to 0.

Are there any alternate forms of this equation?

Yes, this equation can also be written as 2012 + (a/b)((b-c)/c)((c-a)/a), which is equivalent to the original form but may be easier to read and understand.

How can this equation be solved?

The equation can be solved by substituting numerical values for the variables and then using the order of operations (parentheses, multiplication/division, addition/subtraction) to calculate the final answer. Alternatively, it can also be solved using a scientific calculator or a computer program.

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