What are the conditions for solving (a+b)^(-c)?

  • Thread starter Pietair
  • Start date
In summary, the conversation involved a person asking for help with a mathematical equation and another person providing a possible solution. The equation involved finding the value of (a+b)^(-c) and showing that it is equal to (1/a) * (1/(1+bcos(c))). The second person requested clarification on the statements and stated that they are not equal. The first person then asked if there are any conditions to make them equal, and the second person suggested providing a counterexample to show that it is impossible to prove the equality.
  • #1
Pietair
59
0
Good day,

How do I work out (a+b)^(-c)?

Thanks.
 
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  • #2


In my case, c = 1, so I have got: (a+b)^-1
 
  • #3


Well, what does [itex] x ^{-1} [/itex] represent?
 
  • #4


(1/x).

I have got the equation:
r = 1/(a + bcos(c))

This should be equal to:
r = (1/a) * (1/(1+bcos(c)))

I just can't figure out why.
 
  • #5


To be straight that I understand: you have

[tex]
r = \frac 1 {a + b \cos{c}}
[/tex]

and need to show that this equals

[tex]
r = \left(\frac 1 a\right) \left( \frac 1 {1 + b \cos{c}}\right)
[/tex]

If your statements are the ones I've written here, they aren't equal.
 
  • #6


Exactly.
 
  • #7


Are there some type of conditions? If not, just write down a counterexample, therefore showing it's impossible to prove it (ie. a not = 1, b, c in reals)
 

1. What is the formula for solving (a+b)^(-c)?

The formula for solving (a+b)^(-c) is 1/(a+b)^c.

2. How do I simplify (a+b)^(-c)?

To simplify (a+b)^(-c), you can rewrite it as 1/(a+b)^c and then use the rules of exponents to simplify further.

3. Can (a+b)^(-c) be negative?

Yes, (a+b)^(-c) can be negative if both a and b are negative and c is an odd number. For example, if a=-2, b=-3, and c=3, then (a+b)^(-c) would be -1/125.

4. What if c is a fraction in (a+b)^(-c)?

If c is a fraction, for example c=1/2, then (a+b)^(-c) can be rewritten as 1/sqrt(a+b) and simplified using the rules of exponents.

5. How do I solve (a+b)^(-c) if a, b, and c are variables?

If a, b, and c are variables, then you can use algebraic manipulation and the rules of exponents to simplify (a+b)^(-c) as much as possible. If a more specific solution is needed, you can substitute in numerical values for the variables and solve using a calculator or computer program.

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