Difference between revisions of "AoPS Wiki talk:Problem of the Day/September 21, 2011"
(Verb-tense aggrement, can't resist :P) |
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and thus, isolating the square root and squaring, | and thus, isolating the square root and squaring, | ||
<cmath>x=(x-2)^2=x^2-4x+4</cmath> | <cmath>x=(x-2)^2=x^2-4x+4</cmath> | ||
| − | and therefore <math>x^2-5x+4=0</math>. The sum of the roots of this equation, by [[Vieta's formulas]], | + | and therefore <math>x^2-5x+4=0</math>. The sum of the roots of this equation, by [[Vieta's formulas]], is <math>\boxed{5}</math>. |
Latest revision as of 18:28, 21 September 2011
We see, after substitution, that
![\[x=\sqrt{x}+2\]](http://latex.artofproblemsolving.com/3/6/7/367fe5cfd41e070077cabdcebc29e4c3d3181c81.png)
and thus, isolating the square root and squaring,
![\[x=(x-2)^2=x^2-4x+4\]](http://latex.artofproblemsolving.com/6/0/c/60cdcd41f3165ecf865f65a5e9b3a9b3b642bdc3.png)
and therefore 
. The sum of the roots of this equation, by Vieta's formulas, is 
.
