Difference between revisions of "Mock AIME I 2015 Problems/Problem 2"
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By rearranging the values, it is possible to attain an | By rearranging the values, it is possible to attain an | ||
| − | x= 3^ | + | <math>x= 3^ {65/17}</math> |
and | and | ||
| − | y= 3^ | + | <math>y= 3^ {33/17}</math> |
Therefore, a/b is equal to 25/61, so 25+41= 061 | Therefore, a/b is equal to 25/61, so 25+41= 061 | ||
| + | |||
| + | Ignore this solution as it is incorrect - blunderbro | ||
| + | Solution above checked by blunderbro | ||
| + | Note: It is correct this one was the first one posted but was incorrect. | ||
Revision as of 02:22, 9 January 2017
Problem
Suppose that 
and 
are real numbers such that 
and 
. The value of 
can be expressed in the form 
where 
and 
are positive relatively prime integers. Find 
.
Corrected Solution and Answer
Use the logarithmic identity 
to expand the assumptions to
and
Solve for the values of 
and 
which are respectively 
and 
The sought ratio is
The answer then is 
Solution by D. Adrian Tanner (Original solution and answer below)
Original Solution
By rearranging the values, it is possible to attain an
and
Therefore, a/b is equal to 25/61, so 25+41= 061
Ignore this solution as it is incorrect - blunderbro Solution above checked by blunderbro Note: It is correct this one was the first one posted but was incorrect.
