Answer:
b. x² + 2x - 2,115 = 0
Step-by-step explanation:
If you let x represent the smaller number, then the larger one is 2 more, and their product is ...
x(x +2) = 2115
Subtracting 2115 and eliminating parentheses, you get ...
x² +2x -2115 = 0
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Comment on this equation
My favorite way to work problems like this is to use x to represent the average of the numbers. Then the equation is ...
(x -1)(x +1) = 2115
x^2 -2116 = 0
The square root of 2116 is 46, so the numbers are 45 and 47. This quadratic is a lot easier to solve than the one offered by the answer choices.
Usually, I don't bother to add 1, since √2115 is very close to √2116, so the answer becomes obvious just by taking the root of 2115. (It is 45.99.)
