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