Решите систему уравнений [latex] \left \{ {{ 4^{x} *4^{y} =64} \atop { 4^{x} -4^{y} =63}} \right. [/latex]

4^х • 4^у = 64 4^х - 4^у = 63 -------------------- 4^х = а ; 4^у = b ; a > 0 ; b > 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 ( < 0 ) a = 1 + 63 = 64 4^x = a ==> 4^x = 64 = x = 3 4^y = b ==> 4^y = 1 ==> y = 0 Ответ ( 3 ; 0 )