Question 145093
If you try to solve by completing the square, you'll see that in order to get
{{{x^2+y^2=65}}}  to be a square on the left hand side, you'll need to add
{{{(2)xy}}} on both sides. And we are given as {{{(1/2)xy=14}}}

So
{{{x^2+y^2=65}}} 
{{{x^2+2xy+y^2=65 + 2xy}}} 
{{{x^2+2xy+y^2=65 + 4*(1/2)xy}}}
{{{x^2+2xy+y^2=65 + 4*14}}}
{{{(x + y)^2 = 121}}}

{{{(x + y) = sqrt(121)}}}

(x + y) = (+-)11

I don't see that as any of your choices :(