SOLUTION: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. The product of two consecutive positive odd integers is one less than tw

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. The product of two consecutive positive odd integers is one less than tw      Log On


   

Question 299771: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
The product of two consecutive positive odd integers is one less than twice their sum. Find the integers. show work I am really confused with this please help me!!!
thanks

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The product of two consecutive positive odd integers is one less than twice their sum.
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Note: Odd integers are always one less than
or one more than an even integer.
Even integers are always a multiple of 2.
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Your Problem:
1st: 2x-1
2nd: 2x+1
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Equation:
product = 2(sum) - 1
(2x-1)(2x+1) = 2(2x-1+2x+1)-1
4x^2-1 = 2(4x) -1
4x^2 = 8x
4x(x-2) = 0
x = 0 or x = 2
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If x = 0:
1st = 2x-1 = -1
2nd = 2x+1 = 1
Since you want "positive odd integers", x = 0 is not a solution.
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If x = 2:
1st = 2x-1 = 3
2nd = 2x+1 = 5
This pair is the only solution.
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Cheers,
Stan H.