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 1
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 and the coefficient of is . From these two observations, we now create two new equations. Solving either equation and then checking with the other will reveal that . ~kingme271
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 |