2^( 4х - 1 ) + 2^( 4х - 2 ) - 2^( 4х - 3 ) = 160
2^4х•( ( 2^-1 ) + ( 2^( - 2 ) - 2^( - 3 ) ) = 160
2^4х•( ( 1/2 ) + ( 1/4 ) - ( 1/8 )) = 160
1/2 + 1/4 - 1/8 = 4/8 + 2/8 - 1/8 = 5/8
2^4х • ( 5/8 ) = 160
2^4х = 160 : ( 5/8 )
2^4х = 256
2^4х = 2^8
4х = 8
Х = 2
Прибавим и отнимем n²
(n^5-n²)+(n²+n+1)=n²(n³-1)+(n²+n+1)=n²(n-1)(n²+n+1)+(n²+n+1)=
=(n²+n+1)(n³-n²+1)
{y=x²-2x
{2x-3y=0
{y=x²-2x
{2x=3y
{y=x²-2x
{y=2x/3
x²-2x=2x/3
x²-2x-2x/3=0
x²-8x/3=0
x(x-8/3)=0
x(1)=0 x(2)=8/3=2 2/3
у(1)=2*0/3=0 у(2)=2*(8/3)/3=16/9=1 7/9
(0;0) и (2 2/3; 1 7/9)
Ответ: 2 решения