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April 19th, 2018, 02:44 AM   #1
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equation with exponent

Hi everyone,
I just have a doubt when solving the following. Here is what I've done.

2x^2=18
x^2=18/2
x^2=9
x=sqrt9
x=3

My doubt is if the answer is only 3 or -3 is also an answer because of the square root.

Thank you
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April 19th, 2018, 03:02 AM   #2
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It's easy to check, isn't it? 3^2= 9, 2(9)= 18 so 3 is a solution. (-3)^2= 9, 2(9)= 18 so -3 is also a solution. Both 3 and -3 are solutions.
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April 19th, 2018, 03:04 AM   #3
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Originally Posted by Country Boy View Post
It's easy to check, isn't it? 3^2= 9, 2(9)= 18 so 3 is a solution. (-3)^2= 9, 2(9)= 18 so -3 is also a solution. Both 3 and -3 are solutions.
thank you! I just wanted to make sure !
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April 19th, 2018, 03:48 AM   #4
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Note though that $\sqrt{9} = 3$ and not $-3$. The square root is by definition always positive. However, the solutions to $x^2=9$ are both $3$ and $-3$. Crucial distinction!
Thanks from Country Boy
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April 19th, 2018, 08:07 AM   #5
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Quote:
Originally Posted by Micrm@ss View Post
Note though that $\sqrt{9} = 3$ and not $-3$. The square root is by definition always positive. However, the solutions to $x^2=9$ are both $3$ and $-3$. Crucial distinction!
thanks. That actually clarifies a lot!
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April 20th, 2018, 11:09 AM   #6
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That's why you need the "$\displaystyle \pm$" when you say that "the solution to $\displaystyle x^2= a$ is $\displaystyle x= \pm\sqrt{a}$".
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