4*0,5^(x(x+3))=0,25^2x

Question

4*0,5^(x(x+3))=0,25^2x

Answer 1

4 * 0,5 ^ ( X ( X + 3 )) = 0,25 ^ 2X 
( 2 ^ 2 ) * ( 2 ^ - 1 ) ^ ( X ( X + 3 )) = ( 2 ^ - 2 ) ^ 2X 
( 2 ^ 2 ) * ( 2 ^ ( - X ( X + 3 )) = 2 ^ ( - 4X ) 
2 ^ ( 2 - X^2 - 3X ) = 2 ^ ( - 4X ) 
2 - X^2 - 3X = - 4X 
X^2 - X - 2 = 0 
D = 1 + 8 = 9 
√ D = 3 
X1 = ( 1 + 3 ) : 2 = 2 
X2 = ( 1 - 3 ) : 2 = - 1 
ОТВЕТ 2 ; - 1