1973 AHSME Problems/Problem 10
Problem
If is a real number, then the simultaneous system
has no solution if and only if is equal to
Solutions
Solution 1
Add up all three equations to get If , then equation results in . That has no solutions, so the answer is .
Solution 2
From the first equation, Substitute that in the second equation to get Substitute that in the third equation to get (1+n^3)x + n - n^2 = 1$$ (Error compiling LaTeX. Unknown error_msg) If , then equation results in . That has no solutions, so the answer is .
See Also
1973 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AHSME Problems and Solutions |