1963 TMTA High School Algebra I Contest Problem 19
Problem
If the symbol is read "the absolute value of
" and is equal to
when
and is equal to
when
which of the following is always true?
Solution
Examine the validity of the statements one by one. simplifies to
which is false.
is not true in all cases (specifically, one case where it would be true is
and
simplifies to
which is false.
simplifies to
which is true.
Finally, simplifies to
which is false.
The only true statement is
See Also
1963 TMTA High School Mathematics Contests (Problems) | ||
Preceded by Problem 18 |
TMTA High School Mathematics Contest Past Problems/Solutions | Followed by Problem 20 |