Question

Решите уравнение


1) 5^x-1+5^x+1=130

2) 7*3^2x-6*3^x-1=0

Answer 1

$5^{x-1}+5^{x+1}=130 \ \ frac{1}{5} cdot 5^x+5cdot5^x=130 \ \ 5^x+25cdot5^x=130cdot5 \ \ 26cdot5^x=130cdot5 \ \ 5^x=5^2 \ \ x=2$

$7cdot3^{2x}-6cdot3^x-1=0 \ \ 3^{x}=t(t>0) \ \ 7t^2-6t-1=0 \ \ D=b^2-4ac=64 \ \ t_1=- frac{1}{7} ;,,,,,,,,,,,,t_2=1 \ \ 3^x=1$

$x=0$