2 ^ x - 2 ^ y = 24
x + y = 8
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y = 8 - x
2 ^ x - 2 ^ ( 8 - x ) = 24
2 ^ x = a ; 2 ^ ( - x ) = 1 / a
a - 2 ^ 8 * ( 1 / a ) = 24
a - ( 256 / a ) = 24
a ≠ 0
a² - 256 = 24a
a² - 24a - 256 = 0
D = 576 + 1024 = 1600 = 40²
a1 = ( 24 + 40 ) : 2 = 64 : 2 = 32
a2 = ( 24 - 40 ) : 2 = - 8
2 ^ x = 32
2 ^ x = 2 ^ 5
x = 5
2 ^ x = - 8
2 ^ x = 2 ^ - 3
x = - 3
y = 8 - x
y1 = 8 - 5 = 3
y2 = 8 + 3 = 11
Ответ ( 5 ; 3 ) ; ( - 3 ; 11 )