2002 AMC 12P Problems/Problem 10
Problem
Let For how many in is it true that
Solution
Divide by 2 on both sides to get Substituting the definitions of , , and , we may rewrite the expression as We now simplify each term separately using some algebraic manipulation and the Pythagorean identity.
We can rewrite as , which is equivalent to
As for , we may factor it as which can be rewritten as , and then as , which is equivalent to
Putting everything together, we have or .
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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All AMC 12 Problems and Solutions |
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