Срочно 40балов 9^x+16^x<25*12^2x-1

Question

Срочно 40балов
9^x+16^x<25*12^2x-1

Answer 1

3^2x + 4^2x -25*12^(2x-1) < 0 
3^2x + 4^2x -25*12^x*12^-1 <0<br>3^2x + 4^2x -25* *(3*4)^x * 12^-1 < 0
3^2x + 4^2x -25* 3^x*4^x*12^-1 < 0 | : 4^2x
(3/4)^2x +1 - 25*(3/4)^x*12^-1 < 0
(3/4)^x = t
t² +1 - 25/12 *t < 0 |*12
12t² -25t +12 < 0
D = 49,  t1 = 32/24 =4/3, t2 = 18/24 = 3/4
3/4 < t < 4/3
3/4 > (3/4)^x  > 4/3
 -1< x < 1