SOLUTION: There are two positive numbers such that one is 6 less than twice the other.The difference of the squares of the two numbers is 1311.Find the numbers.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: There are two positive numbers such that one is 6 less than twice the other.The difference of the squares of the two numbers is 1311.Find the numbers.      Log On


   

Question 396624: There are two positive numbers such that one is 6 less than twice the other.The difference of the squares of the two numbers is 1311.Find the numbers.
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi

two positive numbers such that one is 6 less than twice the other

Let x and (2x-6) represent the numbers

Question states***

 (2x-6)^2 - x^2 = 1311

solving for x

4x^2 - 24x + 36 - x^2 = 1311

 3x^2 - 24x + 36 = 1311

 3x^2 -24x - 1275 = 0

  x^2 - 8x - 425   

x+=+%288+%2B-+sqrt%28+1764+%29%29%2F%282%29+

  x = (8 ± 42)/2

 x = -17 and x = 25  Tossing out negative solution 

   x = 25, the other number is 44  (2*25-6)



CHECKING our Answer

 1936 - 625 = 1311