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Question 242628: The product of two consecutive odd integers is 2 less than six times their sum. Can you find the two integers.
I thought I could solve but having trouble.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Start by defining what you know.
When working with consecutive digits, x & x+1 are the best choices for solving with one unknown.
BUT, we are told they are consecutive ODD digits, so we'll use x & x+2.
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The sum = x + x+2 = 2x + 2 = 2(x+1)
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The product is x * (x + 2) = x^2 + 2x
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The product is 2 less than the 6 times the sum, so 6 times the sum = product + 2.
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Combining what we know...
Six times the sum: 6(2x + 2) = 12(x+1) = 12x + 12
12x + 12 = x^2 + 2x + 2
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Subtract (12x + 12) from both sides.
0 = x^2 + 2x + 2 - 12x - 12
Combining like terms.
0 = x^2 - 10x - 10
OR
x^2 - 10x - 10 = 0
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Since this does NOT factor, there are no integer solutions.
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