1955 AHSME Problems/Problem 19
Contents
[hide]Problem 19
Two numbers whose sum is and the absolute value of whose difference is are roots of the equation:
Solution
The first two hints can be expressed as the following system of equations: From this, we can clearly see that , and that .
Since quadratic equations can generally be expressed in the form of , where a and b are roots, the correct quadratic, once factored, would look like
Expanding the above equation gets us
Solution 2
Let the roots of the equation be and . Therefore, we can set up a system of equation: Therefore, we get and . So,
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See Also
1955 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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