Continued root of 2

Jun 2010
3
0
Hey guys,

I'm having trouble with this question here.

Capture.PNG

I have to find the value of the continued root of 2 (shown in image) algebraically. Could someone please walk me through it?

p.s. the question gives a hint saying "Find X^2 in terms of X"

Thanks ^_^
 

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MHF Hall of Honor
Mar 2010
2,340
821
Chicago
Hey guys,

I'm having trouble with this question here.

View attachment 18036

I have to find the value of the continued root of 2 (shown in image) algebraically. Could someone please walk me through it?

p.s. the question gives a hint saying "Find X^2 in terms of X"

Thanks ^_^
First note that X can't be negative, because of the definition of \(\displaystyle \sqrt{}\). Then square both sides. What do you see?
 
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Jun 2010
3
0
Well, wouldn't it be:

X^2 = 2 + *continued root*?

or does squaring it get rid of more than just one surd?
 
Jun 2010
3
0
OH WAIT i see it now....

X^2 = 2 + X
X^2 - X - 2 = 0
(X-2)(X+1) = 0

so X = 2 or X = -1

so it must equal 2 because it can't be negative

=D thanks