SOLUTION: The product of 2 consecutive intergers is 41 more than their sum. find the intergers

Question 283197: The product of 2 consecutive intergers is 41 more than their sum. find the intergers
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Two consecutive numbers can be defined as x and y, but a better choice is x and x+1.
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The product of the two numbers is: x(x+1). We are told this 41 more than the sum.
The sum of the two numbers is: x + (x+1).
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So the equation we need to solve is:
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x(x+1) = x+(x+1)+41
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x^2 +x = 2x + 42
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subtract 2x from both sides
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x^2 +x -2x = 2x-2x + 42
x^2 -x = 42
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subtract 42 from both sides
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x^2 -x -42 = 42-42 = 0
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factor
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(x-7)(x+6) = 0
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x = 7 or -6
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We have to check both solutions by substituting these values into the equation.
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7(7+1) = 7+(7+1)+41 ??
7*8 =56
7+8 + 41=56
Correct
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-6(-6+1)=-6+(-6+1)+41 ??
36 -6 = -6 -6 + 42 ??
30 = 30
Correct.
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Answer the consecutive integers are either 7 and 8 OR -6 and -5.
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Done
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