SOLUTION: Hello! So I'm having a hard time on this problem. I know it involves some stuff from Algebra I, but my mind's not in the right place today. So here goes: Find 3 numbers that have a

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Question 1039297: Hello! So I'm having a hard time on this problem. I know it involves some stuff from Algebra I, but my mind's not in the right place today. So here goes: Find 3 numbers that have a sum of 30 and a product of 910, and form an arithmetic sequence. Thanks!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
A possible way to get lost from mistakes is to perform substitution too early.
Substituting for d may be easier than for x.

Three numbers in arithmetic sequence: system%28x%2Cx%2Bd%2Cx%2B2d%29
and their sum: x%2Bx%2Bd%2Bx%2B2d=30
3x%2B3d=30
x%2Bd=10
from which you could later use highlight_green%28d=10-x%29.

The product of 910:
highlight_green%28x%28x%2Bd%29%28x%2B2d%29=910%29
NOW SUBSTITUTE FOR d.
x%28x%2B10-x%29%28x%2B2%2810-x%29%29=910
and skipping the simplification steps,
highlight_green%28highlight_green%28x%5E2-20x%2B91=0%29%29

%28x-13%29%28x-7%29=0
system%28Either%2Cx=13%2COR%2Cx=7%29
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What can be the common difference, d? Do they both work? Maybe.
If x=13, then d=-3;
If x=7, then d=3.

Note from description, the sum must be positive and the product must be positive.
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13, 10, 7
OR
7, 10, 13
Are the numbers.
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