2 ^ x + 2 ^ y = 10
x + y = 4
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x = 4 - y
2 ^ ( 4 - y ) + 2 ^ y = 10
2 ^ y = a ; 2 ^ ( - y ) = 1 / a
16 * ( 1/ a ) + a = 10
( 16 + a^2 ) / a = 10
16 + a^2 = 10a
a^2 - 10a + 16 = 0
D = 100 - 64 = 36 = 6^2
a1 = ( 10 + 6 ) : 2 = 8
a2 = ( 10 - 6 ) : 2 = 2
2 ^ y = 8 ==> 2 ^ y = 2 ^ 3 ==> y = 3
2 ^ y = 2 ==> y = 1
x = 4 - y
x1 = 4 - 3 = 1
x2 = 4 - 1 = 3
Ответ ( 1 ; 3 ) ; ( 3 ; 1 )