Reducing a mathematical expression

In summary, the person is asking for help in reducing an equation and is struggling with the square root part. They are unsure if there is a technique for dealing with this type of equation. There may be a mistake in the original equation and the person suggests multiplying both expressions out to see if they match.
  • #1
ralden
85
0
Hi guys i need your help!

How can i reduce this equation:

(Nd-Na)*[B*sqrt((Nd-Na)^2) + n^2) - sqrt((Na-Nd)^2) + n^2)]

into this:
(B-1)*(Nd-Na) + (B+1)*sqrt(Nd-Na)^2) + n^2)?

I'm totally depressed, I'm always stocked in sqrt part of the equation:
if there's a techniques in dealing this kind of equation please let me know. thanks.
 
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  • #2
ralden said:
Hi guys i need your help!

How can i reduce this equation:

(Nd-Na)*[B*sqrt((Nd-Na)^2) + n^2) - sqrt((Na-Nd)^2) + n^2)]

into this:
(B-1)*(Nd-Na) + (B+1)*sqrt(Nd-Na)^2) + n^2)?
Neither of these is an equation (there's no = in either).
Beyond that I don't think you can manipulate the first expression into the second.

##(N_d - N_a) \left[B(\sqrt{(N_d - N_a)^2 + n^2} - \sqrt{(N_a - N_d)^2 + n^2}\right]##
##= (N_d - N_a) \sqrt{(N_d - N_a)^2 + n^2} (B - 1)##

I don't see any obvious way to turn the above into what you're supposed to get. It's possible you have a mistake in what you show for the first expression above.

Note that ##(N_a - N_d)^2 = (N_d - N_a)^2##, so the first radical in the original expression is equal to the second radical.

ralden said:
I'm totally depressed, I'm always stocked in sqrt part of the equation:
Don't you mean you're always stuck?
ralden said:
if there's a techniques in dealing this kind of equation please let me know. thanks.
 
  • #3
There are unmatched parenthesis in both expressions. You should check that. Depending on the parenthesis inside the sqrt, the sqrt may disappear. Multiply both expressions out and see it the individual terms match up. If the sqrt didn't disappear, leave it unchanged. If the terms don't match, the expressions are not identical.
 

1. What is the purpose of reducing a mathematical expression?

Reducing a mathematical expression simplifies it to its most basic form, making it easier to understand and work with. It also helps to identify patterns and relationships within the expression.

2. How do you reduce an algebraic expression?

To reduce an algebraic expression, you need to combine like terms by adding or subtracting them. You can also use the distributive property to simplify expressions by factoring out common terms.

3. Can reducing an expression change its meaning?

No, reducing an expression does not change its meaning. It simply simplifies the expression without altering its value.

4. What are the benefits of reducing a mathematical expression?

Reducing a mathematical expression can make it easier to solve equations, identify patterns and relationships, and make complex problems more manageable. It also helps to improve mathematical skills and understanding.

5. Are there any rules for reducing mathematical expressions?

Yes, there are rules for reducing mathematical expressions, such as the commutative, associative, and distributive properties. It is important to follow these rules to ensure the accuracy of the reduced expression.

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