Question

Решите:
1) 16^x-9=1/2
2) (5x-3)^2=(5x+13)^2
3) x-6/7x+3=x-6/5x-1

Answer 1

$1) 16^{x-9}= frac{1}{2} \ \ (2^4)^{x-9}=2^{-1} \ \ 2^{4x-36}=2^{-1} \ \ 4x-36=-1 \ \ 4x=-1+36 \ \x=35 \ \ x= frac{35}{4} \ \ x=8 frac{3}{4}$

$2) (5x-3)^2=(5x+13)^2 \ \ 25 x^{2} -30x+9=25 x^{2} +130x+169 \ \ 130x+30x=-169+9 \ \ 160x=-160 \ \ x=-1$

3) ОДЗ
7х+3≠0
х≠-3/7
5х-1≠0
5х≠1
х≠0,2

$frac{x-6}{7x+3} = frac{x-6}{5x-1} \ \ x-6=0 \ \ x_1=6 \ \ frac{1}{7x+3}= frac{1}{5x-1} \ \ 5x-1=7x+3 \ \ 7x-5x=-1-3 \ \ 2x=-4 \ \ x_2=-2$