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Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 14, 2011"

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{{:AoPSWiki:Problem of the Day/June 14, 2011}}
 
{{:AoPSWiki:Problem of the Day/June 14, 2011}}
 
==Solution==
 
==Solution==
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{{potd_solution}}
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We multiply both sides by <math>x+1</math> so that the equation is:
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<math>\sqrt{x^2+7x+6} = \sqrt{7x+15}</math>
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Squaring both sides and simplifying, we get:
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<math>x^2 = 9</math>
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The solutions to this equation are <math>\pm3</math>.  However, we plug in <math>-3</math> in the original equation and find that there is an imaginary number in the expression.  So the answer is <math>\framebox{3}</math>.

Latest revision as of 22:04, 13 June 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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