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AoPS Wiki talk:Problem of the Day/June 14, 2011

Problem

AoPSWiki:Problem of the Day/June 14, 2011

Solution

We multiply both sides by $x+1$ so that the equation is:

$\sqrt{x^2+7x+6} = \sqrt{7x+15}$

Squaring both sides and simplifying, we get:

$x^2 = 9$

The solutions to this equation are $\pm3$. However, we plug in $-3$ in the original equation and find that there is an imaginary number in the expression. So the answer is $\framebox{3}$.

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