Math CentralQuandaries & Queries


Question from Katie:

what 2 numbers add to get 7 and multiply to get 2?

Hi Katie,

If you have read my response to other questions of this type you will know that I prefer a solution that doesn't use algebra. This example shows that for some problems you need the power of algebra.

Suppose that the two numbers are $x$ and $y.$ The sum of these numbers is 7 so

\[x + y = 7.\]

You also know that their product is 2 so

\[xy = 2.\]

Solve the first equation for $y,$ substitute into the second equation and solve the resulting quadratic equation.

I hope this helps,

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