Question

$left { {{2^{2+x-y^2} }+2^{3x+y^2}= 2^{2x+2}}atop {3^{6-2x-3y} +13*3^{1+y} =13*3^{3-x-y}+3^{x+3y}}} right.$
Решить систему

Answer 1

$2^{2+x-y^2}+2^{3x+y^2} = 2^{ 2x+2 }\ 3^{6-2x-3y} + 13*3^{1+y} = 13*3^{3-x-y}+3^{x+3y}\\ 2^{2x+2y^2}+4 = 2^{y^2+x+2}\ -3^{-2x-3y}(3^{x+2y} -27 )( 3^{x+2y} - 9 ) (3^{x+2y}-3)=0\ x+2y=3\ x+2y=2\ x+2y=1 \\ x=3-2y\ x=2-2y\ x=1-2y\\ 2^{2(3-2y)+2y^2}+4=2^{y^2-2y+5}\ 2^{2(2-2y)+2y^2}+4=2^{y^22-2y+2}\ 2^{2(1-2y)+2y^2}+4=2^{y^2+1-2y+2}\ y^2=2y\\ y=0;2\ x=-3;1$