SOLUTION: two positive numbers are consecutive odd integers. the square of the smaller is 10 less than 5 times the larger. Find the integers.

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Question 145053: two positive numbers are consecutive odd integers. the square of the smaller is 10 less than 5 times the larger. Find the integers.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
two positive numbers are consecutive odd integers. the square of the smaller is 10 less than 5 times the larger. Find the integers
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1st: 2x+1
2nd: 2x+3
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EQUATION:
(2x+1)^2 = 5(2x+3)-10
4x^2 + 4x + 1 = 10x + 5
4x^2 - 6x -4 = 0
2x^2 -3x -2 = 0
2x^2 -4x+x-2 = 0
2x(x-2)+(x-2) = 0
(x-2)(2x+1) = 0
x = 2 or x = -1/2
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If x= 2 or x = 1/2
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If x = 2, 2x+1 = 5 (smaller positive odd integer)
and 2x+3 = 7 (larger positive odd integer)
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If x = 1/2 , 2x+1 = 2 which is not odd
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Only solution:
smaller = 5
larger = 7
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Cheers,
Stan H.