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April 19th, 2018, 02:44 AM  #1 
Newbie Joined: Mar 2018 From: Canada Posts: 14 Thanks: 0  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 
April 19th, 2018, 03:02 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
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.

April 19th, 2018, 03:04 AM  #3 
Newbie Joined: Mar 2018 From: Canada Posts: 14 Thanks: 0  
April 19th, 2018, 03:48 AM  #4 
Senior Member Joined: Oct 2009 Posts: 770 Thanks: 276 
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!

April 19th, 2018, 08:07 AM  #5 
Newbie Joined: Mar 2018 From: Canada Posts: 14 Thanks: 0  
April 20th, 2018, 11:09 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
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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