Решите систему уравнений [tex] \left \{ {{2^x+2^y=10} \atop {x+y=4}} ight. [/tex]

2^x + 2^y = 10x+y=4-------------x=4-y2^(4-y) + 2^y = 102^4/2^y + 2^y = 1016/2^y + 2^y = 1016 + (2^y)^2 - 10*2^y = 02^y=t t>0t^2 - 10y + 16 =0D=100-4*16=36=6^2t12= (10+-6)/2 = 8 22^y=2y=1x+y=4x=32^y=82^y=2^3y=3x+y=4x=1ответ (1 3) (3 1)