2018 UNCO Math Contest II Problems/Problem 3
Problem
Find all values of that have the property that if
lies on the hyperbola
,
then so does the point
.
Solution
We can write a system of equations -
Expanding the second equation, we get .
Since we want this to look like , we plug in B's that would put it into that form. If we plug in
, things cancel, and we get
. So
~Ultraman
Solution 2 (Grinding)
As with Solution 1, we create a system of equations.
Through expanding the second equation, we get . Since
, we have
. The
terms on each side cancel out, so the equation becomes
The coefficient of
on the RHS is 0 and the coefficient of
is 2. From these two observations, we now create two new equations.
Solving either equation and then checking with the other will reveal that
.
See also
2018 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |