Continued root of 2
I'm having trouble with this question here.
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"
First note that X can't be negative, because of the definition of . Then square both sides. What do you see?
Originally Posted by DrizzlyDays
Well, wouldn't it be:
X^2 = 2 + *continued root*?
or does squaring it get rid of more than just one surd?
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