Question 821548
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
Twice the product of two numbers {{{green(x)}}} and {{{green(y)}}} is {{{highlight(highlight(56))}}} 0r  2xy = 56, {{{x = 28/y}}}
The sum of their squares is 65.   {{{x^2 + y^2 = 65}}} 
<u>If both numbers are positive, what is the sum of the two numbers </u>?
 {{{x^2 + y^2 = 65}}}        |Substituting for x
 {{{(28/y)^2 + y^2 = 65}}}
   {{{(28)^2/(y)^2 + y^2 = 65}}}  |Multiplying thru by y^2 so as all denominators = 1
{{{(28)^2 + y^4 = 65y^2}}}
{{{y^4 - 65y^2 + 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"
<u>the sum of the two numbers </u> is  11