Распишите полностью решение

$\left \{ {{log _{4}x+log _{4} y=log _{4} +log _{4} 9/(1)} \atop {2 ^{ \frac{x+y}{2} } =1024/(2)}} \right. \\ \\ log _{4}x+log _{4} y=log _{4} +log _{4} 9 \\ log _{4} (x*y)=log _{4} (4*9) \\ log _{4} (x*y)=log _{4} 36 \\ x*y=36 \\ \\ (2)2 ^{ \frac{x+y}{2} } =1024 \\ 2 ^{ \frac{x+y}{2} } = 2 ^{10} \\ \frac{x+y}{2} =10/*2 \\ x+y=20$

$\left \{ {{x*y=36} \atop {x+y=20}} \right. \\ \\ \left \{ {{x*y=36/(3)} \atop {y=20-x}} \right. \\ \\ (3)x*(20-x)=36\\20x- x^{2} =36\\20x- x^{2} -36=0\\- x^{2} +20x-36=0/*(-1)\\ x^{2} -20x+36=0\\D=400-144=256 \\ \sqrt{D} =16 \\ x_{1} = \frac{20-16}{2} =2 \\ x_{2} = \frac{20+16}{2} =18 \\$

$y _{1} =20-2=18 \\ y _{2} =20-18=2 \\ \\ \left \{ {{ x_{1} } =2\atop {y _{1}=18 }} \right. \left \{ {{ x_{2} } =18\atop {y _{2}=2 }} \right. \\ \\ x_{1} + x_{2} =2+18=20$

Ответ: 20