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The product of two consecutive odd integers is 2,115. Find the integers. Which of the following quadratic equations could be used to solve the word problem?

a. x² + x - 2,115 = 0b. x² + 2x - 2,115 = 0c. x² + 2x + 2,115 = 0

1 Answer

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Answer:

b. x² + 2x - 2,115 = 0

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.)

User Ewaren
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