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SOURCE:COMPETITION Number of Problems: 13. FOR PRINT ::: (Book)
For the nonzero numbers a, b, and c, define
Find .
The symbolism denotes the largest integer not exceeding . For example, and . Compute
The first three values in the sum are equal to the next five equal to the next seven equal to and the last one equal to For example, since any square root of a number less than must be less than Sum them all together to get
Given that a, b, and c are non-zero real numbers, define , find .
. Our answer is then .
Alternate solution for the lazy: Without computing the answer exactly, we see that , , and . The sum is , and as all the options are integers, the correct one is obviously .
For real numbers and , define . What is the value of
?
For any three real numbers , , and , with , the operation is defined by: What is ?
For real numbers and , define . What is ?
Since :
For each pair of real numbers , define the operation as
.
What is the value of ?
Define . What is ?
By the definition of , we have . Then . The answer is .
Since , it follows that , and