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 Algebra
 Why is one answer - or + and the other is just +?
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Nichelle1012
Junior Member

USA
5 Posts

Posted - 09/25/2013 :  20:37:43  Show Profile  Reply with Quote
In the equation of (2x-1)(2x+1)=35, x=3 or -3. Note: The original equation was cross multiplication, which was 2x-1 over 7 = 5 over 2x+1. OR 2x-1/ 7 = 5/ 2x+1. That simplifies to (2x-1)(2x+1)=35.

Now, in another equation, which is a over 16 = 4 over a OR a/ 16 = 4/ a, the answer is a=4.

Why is the first solution x= 3 or -3 (negative or positive) and the second solution is a=4 (only positive)? Why is the answer positive or negative for one equation and only positive for the other?
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royhaas
Moderator

USA
3059 Posts

Posted - 09/26/2013 :  11:07:23  Show Profile  Reply with Quote
In the first equation, a = 3 or a = -3 satisfies the original equation. In the second equation, only a = 3 satisfies the original equation.
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 09/26/2013 :  16:09:54  Show Profile  Reply with Quote
In the first one, you have the quadratic equation
4x-1 = 35
that is 4x=36 and finally x=9 which solves to x=+3 and x=-3
The reason, 9 is 3 (3*3=9) and -3 (-3*-3=9)

In the second one, you have a cubic equation
a=64
The solution would be a = 64 and that is only +4 because
4*4*4=64. Note that -4*-4*-4 = -64 and thus, not a cube root of "64"

Basically what is going on is that when you square a number, a negative squared is positive so the negative number is also an answer since it gives you what you want (a positive).
When you cube a number, a negative number cubed is not positive so it is not a solution.

Edited by - the_hill1962 on 09/27/2013 08:36:59
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Nichelle1012
Junior Member

USA
5 Posts

Posted - 09/26/2013 :  17:05:50  Show Profile  Reply with Quote
quote:
Originally posted by the_hill1962

In the first one, you have the quadratic equation
4x-1 = 35
that is 4x=36 and finally x=9 which solves to x=+3 and x=-3
The reason, 9 is 3 (3*3=9) and -3 (-3*-3=9)

In the second one, you have a cubic equation
a=64
The solution would be a = 64 and that is only +4 because
4*4*4=64. Note that -4*-4*-4 = -64 and thus, not a cube root of "64"

Basically what is going on is that when you square a number, a negative square is positive so the negative is also an answer.
When you cube a number, a negative number cubed is not positive so it is not a solution.





THANKS the_hill1962. You explained everything as if you were a professor. :-)
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