Question

решите уравнение 9^x+4^x=2•6^x

Answer 1

9^x+4^x=2•6^x  /:6^x

9^x = (3^2)^x = 3^2x

4^x = (2^2)^x = 2^2x

6^x = 2^x*3^x

3^x/2^x + 2^x/3^x = 2

3^x/2^x = y > 0

y + 1/y = 2

y^2 - 2y + 1 = 0

(y - 1)^2 = 0

y = 1

(3/2)^x = 1

(3/2)^x = (3/2)^0

x = 0