2008 Mock ARML 1 Problems/Problem 1
Compute all real values of such that .
Let ; then . Because is increasing on , . Using this we can show . Using your favorite method, solve for . However, since , and because the Square Root function's range does not include negative numbers, it follows that the negative root is extraneous, and thus we have .
|2008 Mock ARML 1 (Problems, Source)|
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Square both sides twice leaving:
Then, subtract to set to (from )
Using the rational roots theorem, we get the quadratics:
Seeing that negative roots are extraneous we have:
and as the answers.