SOLUTION: The product of the smaller two of three consecutive integers is equal to 23 plus the largest. Find the integers.

Question 141735This question is from textbook Introductory Algebra
: The product of the smaller two of three consecutive integers is equal to 23 plus the largest. Find the integers. This question is from textbook Introductory Algebra

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The product of the smaller two of three consecutive integers is equal to 23 plus the largest. Find the integers.
:
3 consecutive integers: x, (x+1), (x+2)
:
Write an equation for what it says:
x*(x+1) = 23 + (x+2)
:
x^2 + x = x + 25
:
x^2 + x - x - 25 = 0; arrange as a quadratic equation
:
x^2 - 25 = 0; recognize this as the "difference of square"
Factors to:
(x-5)(x+5) = 0
Two solutions:
x = +5, (5, 6, 7 are the integers)
and
x = -5, (-5, -4 ,-3 can also be the integers.
:
Check both solutions in the original equation

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