SOLUTION: One positive integer is 3 less than twice another. Find these two integers if the difference of their squares is 24.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: One positive integer is 3 less than twice another. Find these two integers if the difference of their squares is 24.      Log On


   

Question 503400: One positive integer is 3 less than twice another. Find these two integers if the difference of their squares is 24.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
y = 2x-3
y^2 -x^2 =24
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substitute
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y^2 = (2x-3)^2
y^2 = 4x^2 -12x +9
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substitute
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4x^2 -12x +9 -x^2 = 24
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3x^2 -12x -15 = 0
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x^2 -4x -5 = 0
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(x-5)(x-1) = 0
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We're only looking for a positive integer, so x=5.
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substitute
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y = 2x -3
y = 7
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Always check your answer.
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y^2 = 7^2 = 49
x^2 = 5^2 = 25
y^2 -x^2 = 24
Correct.
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Answer: The two positive integers are 5 and 7.
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Done.