Решите систему уравнений [tex] left 4^x *4^y =64 atop

4^х 4^у = 64
4^х - 4^у = 63
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4^х = а ; 4^у = b ; a gt; 0 ; b gt; 0
ab = 64
a - b = 63
a = b + 63
b( b + 63 ) = 64
b^2 + 63b - 64 = 0
D = 3969 + 256 = 4225 = 65^2
b1 = ( - 63 + 65 ) : 2 = 1
b2 = ( - 63 - 65 ) : 2 = - 64 ( lt; 0 )
a = 1 + 63 = 64
4^x = a ==gt; 4^x = 64 = x = 3
4^y = b ==gt; 4^y = 1 ==gt; y = 0
Ответ ( 3 ; 0 )