Question 1011843
xy=12, (x^2+y^2)=25 then what is the value of (x+y)2^2
<pre>{{{xy = 12}}}   ;   {{{x^2 + y^2 = 25}}}

Observing {{{x^2 + y^2 = 25}}}, it's obvious that x and y MUST be 3 and 4
Likewise x and y MUST be 3 and 4 as xy = 12

Proving this, we get:
{{{(x + y)^2 = x^2 + 2xy + y^2}}} --------> {{{x^2 + y^2 + 2xy}}}, which becomes: 25 + 2(12) = 25 + 24 = 49
Since {{{(x + y)^2 = 49}}}, then x + y = 7 ------ Square root of each side was taken

I don’t know what {{{(x + y)2^2}}} means but you should be able to determine what’s needed since it was found that: 
{{{(x + y)^2 = 49}}} & {{{x + y = 7}}}, and the following were given: {{{xy = 12}}} & {{{(x^2 + y^2) = 25 }}}