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November 30th, 2017, 03:16 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 619 Thanks: 83  Equation With An Irrational Number
If 2x + x*(square root of 2) = 6, what is x?

November 30th, 2017, 03:21 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,722 Thanks: 600 Math Focus: Yet to find out. 
$x = \dfrac{6}{(2 + \sqrt{2})}$?

November 30th, 2017, 03:35 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
In a little more detail: $\displaystyle 2x+ x\sqrt{2}= (2+ \sqrt{2})x= 6$ Divide both sides by $\displaystyle 2+ \sqrt{2}$ If you don't like that $\displaystyle \sqrt{2}$ in the denominator, rationalize the denominator by multiplying by $\displaystyle \frac{2 \sqrt{2}}{2 \sqrt{2}}$: $\displaystyle \frac{6}{2+ \sqrt{2}}\frac{2 \sqrt{2}}{2 \sqrt{2}}= \frac{6(2 \sqrt{2})}{(2+ \sqrt{2})(2 \sqrt{2}}= \frac{12 6\sqrt{2}}{4 2}= 6 3\sqrt{2}$ 
November 30th, 2017, 03:55 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,334 Thanks: 938  
November 30th, 2017, 04:47 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  
November 30th, 2017, 04:54 PM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
I first misread the problem thinking that the "x" was inside the square root in which case squaring would be the way to go. But it is not, this is just a simple linear equation for x.


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