SOLUTION: Twice the product of two numbers is 56. The sum of their squares is 65. If both numbers are positive, what is the sum of the two numbers?

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Question 821548: Twice the product of two numbers is 56. The sum of their squares is 65. If both numbers are positive, what is the sum of the two numbers?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Twice the product of two numbers green%28x%29 and green%28y%29 is highlight%28highlight%2856%29%29 0r  2xy = 56, x+=+28%2Fy

The sum of their squares is 65.   x%5E2+%2B+y%5E2+=+65 

If both numbers are positive, what is the sum of the two numbers ?

 x%5E2+%2B+y%5E2+=+65        |Substituting for x

 %2828%2Fy%29%5E2+%2B+y%5E2+=+65

   %2828%29%5E2%2F%28y%29%5E2+%2B+y%5E2+=+65  |Multiplying thru by y^2 so as all denominators = 1

%2828%29%5E2+%2B+y%5E4+=+65y%5E2

y%5E4+-+65y%5E2+%2B+784    |Letting S = y^2

   S^2 - 65S + 784 = 0

  (S-49)(S-16) = 0, S is 16,49  and 

y is  4  or  7  and x is  7  0r  4  Note: "both number are positive"

the sum of the two numbers  is  11