Решите систему 5^(2x*y)=625 3^(x-3y)=27 - вопрос №5262533273365837 от Privetcsfvxs 14.09.2021 07:49

Question

Математика: Решите систему 5^(2x*y)=625 3^(x-3y)=27

Privetcsfvxs · Answer

5 ^ ( 2XY ) = 625
5 ^ ( 2XY ) = 5 ^ 4
2XY = 4
XY = 2

3 ^ ( X - 3Y ) = 27
3 ^ ( X - 3Y ) = 3 ^ 3
X - 3Y = 3
X = 3Y + 3

Y * ( 3Y + 3 ) = 2
3Y^2 + 3Y - 2 = 0
D = 9 + 24 = 33 ; √ D = √ 33
Y1 = ( - 3 + √ 33 ) : 6 = - 1/2 + 1/6 √ 33
Y2 = - 1/2 - 1/6 √ 33

X1 = 3 * ( - 1/2 + 1/6 √ 33 ) = - 1,5 + 0,5 √ 33
X2 = 3 * ( - 1/2 - 1/6 √ 33 ) = - 1,5 - 0,5 √ 33